How to Solve Simultaneous Equations Graphically

Last Updated: February 17, 2023

There are a few ways to solve simultaneous equations;^{[1]
X
Research source} one of them is to plot the lines of the 2 equations, thus solving the equation. This article will teach you how to solve simultaneous equations graphically!

Steps

1
Write your 2 equations clearly. Write your 2 equations in an organised, clear way. This will make it easier later.^{[2]
X
Research source}
- In this guide, we are going to use equations 3x+4y=22 and x+2y=2 as an example.
2
In the first equation, let x be 0. Replace x with 0, and solve the equation. This should give you the value of y.
- Using the example before: 3*0+4y=22, which becomes 4y=22, and then y=5½
- You now have your first coordinate, (0 ; 5½)
Advertisement
3
Let y be 0. In the first equation, let y be 0 and solve the equation. This will give you the value of x.
- Using the example: 3x+4*0=22 which becomes 3x=22 which gives us the answer of x=7⅓
- You now have a set of coordinates for your first line, (0 ; 5½) and (7⅓ ; 0)
4
Draw a graph with 4 quadrants. Draw the line of your first equation on it.^{[3]
X
Research source}
5
In the second equation, let x be 0. Then solve the equation, giving you the value of y.
- Using the example, it's 0+2y=2, which becomes 2y=2 and y=1
- First coordinate is now (0 ; 1)
6
Let y be 0. Solve the equation and get the value of x.
- Example: x+2*0=2, which becomes x=2.
- Second coordinate is now (2 ; 0)
7
Draw the line of the second equation on the same graph as before. If needed, increase the length of the 2 lines until they meet.^{[4]
X
Research source}
8
Look at the point in which the 2 lines meet. Get it's coordinates (x ; y). The x coordinate will be the value of x in the equation, and the y coordinate will be the value of y!^{[5]
X
Research source}
- If you've been using the example, the lines should meet at point (18 ; -8). x will be 18, and y will be -8!

Community Q&A

Question

What will be the answer if lines do not intersect?

Donagan

Top Answerer

If the graphed lines do not intersect, the system has no solution. That means there is no set of values for the variables that will work for both equations simultaneously.
Question

How do I guess the number, like x=0 or x=1, etc.?

Donagan

Top Answerer

You don't guess any numbers. You simply use a low number for x (like 0, 1, 2, -1, or -2, for example) so that it's easy to calculate the corresponding value of y.
Question

How do I solve y=2x+1, y=x-5?

Donagan

Top Answerer

Plot both equations on the same graph. The x and y values of the point where the two lines intersect are the solution of the equations.