Finding the Solutions to Systems of Equations

 

First off, what are systems of equations? 

Systems of equations are a pair or more of linear equations working together.

 

What is a linear equation?

A linear is an equation that can be written in the form ax + by = c.

 

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Example of a System of Equations

3x+y= 24

2x+y=12

Step 1: Solve one linear equation

for y in terms of x. 

y=-2x+12

Step 2: Substitute that expression for y

in the other linear equation and solve for x. 

3x+(-2x+12)=24

1x+12=24

x=12

Step 3: Plug x into either equation to find the

y coordinate and solve. Let’s plug

it into our second equation. 

2(12)+y=12

24+y=12

y=-12

The solution is (12, -12)