# when solving a system of equations graphically, when would you need to estimate the solution? explain.

### James

Guys, does anyone know the answer?

get when solving a system of equations graphically, when would you need to estimate the solution? explain. from EN Bilgi.

## Solve systems of equations by graphing (Pre

## Solve systems of equations by graphing

A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

**Example**

{ y=2x+2 y=x−1 {y=2x+2y=x−1

Graph the equations in a coordinate plane

The two lines intersect in (-3, -4) which is the solution to this system of equations.

**Video lesson**

Find the solution of two equations by graphing

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**More classes on this subject**

Pre-Algebra Graphing and functions: Linear equations in the coordinate plane Pre-Algebra Graphing and functions: The slope of a linear function Pre-Algebra Graphing and functions: Graphing linear inequalities

## What are some ways to solve systems of equations graphically?

Answer (1 of 8): For solving a system of simultaneous equations graphically…Firstly represent the system on the graph. & its graphical representation will be a pair of straight lines.. There are 3 possible ways in which these pairs of straight lines are obtained.. (1) either lines will be inter...

What are some ways to solve systems of equations graphically?

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Sort Dhaniram Kesari

I have ideas sometimes.5y

If you're going to solve equations graphically, you're limited to considering systems if 2 equations, or if you’re skilled, 3 dimensions, that is, you're allowed up to 3 variables. More than that and we can't even envision it. The first step would be to graph your equations. So what are you looking for in the graphs? Points of intersection of course! If there are no points of intersection, i.e. the lines are parallel, then the system has no solution.

And since you're graphing, the coordinates are your solution. If you need help finding those coordinates, there are a bunch of ways, e.g. Bisectio

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Naman Mittal Math lover3y

Why solve graphically when you have other better methods. Check out this method and you will be able to solve any linear equation question mentally.

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Manon DeMaagd

Former Secondary Mathematics Teacher (1992–2019)2y

Originally Answered: How do you solve equations graphically?

If you know how to graph on the Cartesian Coordinate Plane (x y axis), then the solution is the point where two lines intersect or two inequalities overlap. It is a great idea to get familiar with the “families” of graphs in order to recognize any translations from the “parent” function given only the equations. Good luck!

Girija Warrier

Studied at Sufficiently EducatedAuthor has 4.3K answers and 9.1M answer views5y

For solving a system of simultaneous equations graphically…Firstly represent the system on the graph. & its graphical representation will be a pair of straight lines..

There are 3 possible ways in which these pairs of straight lines are obtained..

(1) either lines will be intersecting each other, in that case , the coordinates of the point of intersection will be the solution of the system.

(2) or the lines will be parallel. In that case, there won't be any common point to them. Hence there is n...

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Sourabh Soni

Founder and CEO at Www.fundootutor.com (2020–present)Author has 1.1K answers and 1.1M answer views8mo

From this video you will get a knowledge about:- 1. We know that given two lines in a plane, only one of the following three possibilities can happen- 2. The two lines will intersect at one point. 3. The two lines will not intersect however far they are extended i.e., they are parallel. 4. The two lines are coincident lines.

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(Continue reading) Justin Olhipi

MA in Mathematics Education, Central Washington UniversityAuthor has 737 answers and 452.1K answer views5y

Generally, you graph the equations and see where they cross. Your solution is only as good as your graph. Moreover, graphing a system for a solution is generally good for only a few variables. However, sometimes, in some problems that arise in real-world applications, graphing may be the best way to go.

Narasimham Kandanuru

Former lecturer in Civil Engg. at Engg College/polytechnic (1958–1994)Author has 3.4K answers and 557.1K answer views2y

Originally Answered: How do you solve equations graphically?

In a system of linear equations the coordinates of point of intersection when plotted on an axes system. give the solution of unknowns

Dima Ry

Mathematics instructor5y

Assuming you have system of 2 equations with 2 variables, you plot the graph of each equation on the XY-coordinate system.

Graphs will intersect at some point(s) that have coordinates. Those coordinates are solutions.

Alexander Farrugia

Ph.D. in Mathematics, University of Malta (Graduated 2016)Author has 3.2K answers and 19.2M answer viewsUpdated 7y

Related

How do you solve the following system of equations?

## Solving equations graphically (1 of 2) (video)

Sal solves the equation e^x=1/[x(x-1)(x-2)] by considering the graphs of y=e^x and y=1/[x(x-1)(x-2)].

Current time:0:00Total duration:8:03

Solving equations by graphing (Algebra 2 level)

## Solving equations graphically (1 of 2)

Sal solves the equation e^x=1/[x(x-1)(x-2)] by considering the graphs of y=e^x and y=1/[x(x-1)(x-2)]. Created by Sal Khan.

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## Solving equations by graphing (Algebra 2 level)

Interpreting equations graphically

Interpreting equations graphically (example 2)

Practice: Interpret equations graphically

Solving equations graphically (1 of 2)

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Solving equations graphically (2 of 2)

Solving equations graphically

Practice: Solve equations graphically

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## Want to join the conversation?

Log in Peter Wraae Marino 8 years ago

Posted 8 years ago. Direct link to Peter Wraae Marino's post “I don't get it... how is ...”

I don't get it... how is 7.846 and 7.633 within 0.01 ?

• Peter Norby 8 years ago

Posted 8 years ago. Direct link to Peter Norby's post “Those are the values of E...”

Those are the values of E(x) and R(x). You want x within 0.01 of the actual value of x, not E(x) within 0.01 of R(x).

Richard E Boyen Jr 8 years ago

Posted 8 years ago. Direct link to Richard E Boyen Jr 's post “At 2:05 Sal uses his calc...”

At 2:05 Sal uses his calculator and chooses "e" and raises that to a power of 2.1. What is "e" and where did that irrational come from?

• Peter Wraae Marino 8 years ago

Posted 8 years ago. Direct link to Peter Wraae Marino's post “e is a constant, just lik...”

e is a constant, just like PI is a constant. e is something like: 2.71828.... e is the base of natural logarithm. I believe that e stands for Euler's number.

miteshkumar 7 years ago

Posted 7 years ago. Direct link to miteshkumar's post “I have never learned this...”

I have never learned this stuff. are there videos before this that will help me do this?

• Niomi 7 years ago

Posted 7 years ago. Direct link to Niomi's post “This video gives an intro...”

This video gives an introduction to euler's number (e).

https://www.khanacademy.org/math/algebra2/exponential_and_logarithmic_func/continuous_compounding/v/compound-interest-and-e-part-2

This might help too (from wikipedia): The number e is an important mathematical constant that is the base of the natural logarithm. It is approximately equal to 2.71828, and is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series.

https://en.wikipedia.org/wiki/E_(mathematical_constant)

Wrath Of Academy 8 years ago

Posted 8 years ago. Direct link to Wrath Of Academy's post “At the point Sal was look...”

At the point Sal was looking for, the y values change enormously for tiny changes in x. Sal guesses a starting x of 2.1 by looking at the x axis. So would there be a way to use an estimate on the graph for the y axis, in order to go back and get a better starting point for the x value?

• Peter Norby 8 years ago

Posted 8 years ago. Direct link to Peter Norby's post “If you used an inverse fu...”

If you used an inverse function for either R(x) or E(x) , then you could plugin an estimate of maybe 7.8 into that function, to come up with a starting value of x. e^x conveniently has an inverse function, which is ln(x).

ln(7.8) comes up as 2.05412373369554605284 on my calculator, which gives you a **very** good starting point, yes. :)

Kevin Fischer 7 years ago

Posted 7 years ago. Direct link to Kevin Fischer's post “What is the value of e at...”

What is the value of e at 4:07?

• andrewp18 7 years ago

Posted 7 years ago. Direct link to andrewp18's post “e is an irrational number...”

e is an irrational number like π (meaning it cannot be written as the ratio of 2 integers and thus in its decimal form it will go on forever without any pattern). The first few digits of e are:

e ≈ 2.718 Maria 7 years ago

Posted 7 years ago. Direct link to Maria's post “What is "e"? I've run in...”

What is "e"? I've run into it, and I know it's aprox. 2.71812, but what is it's specific "job" in mathematics?

• Sirgargamel24 7 years ago

Posted 7 years ago. Direct link to Sirgargamel24's post “The number represented by...”

The number represented by the variable 'e' is called Euler's Number. In math, it represents the base for something called the natural logarithm, which is a process that counteracts something being raised to a power, much like addition counteracts subtraction.

Abiodun Lawal 7 years ago

Posted 7 years ago. Direct link to Abiodun Lawal's post “Please, how exactly is E(...”

Please, how exactly is E(x)=R(x) within 0.01 ?

• InnocentRealist 6 years ago

Posted 6 years ago. Direct link to InnocentRealist's post “When it's much closer tha...”

When it's much closer than either 2.05 and 2.07.

foxdavid66 8 years ago

Posted 8 years ago. Direct link to foxdavid66's post “What does "within 0.01" m...”

What does "within 0.01" mean exactly?

Guys, does anyone know the answer?