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System of equations
Solving systems of equations using substitution

Solving systems of equations by substitution is one method to find the point that is a solution to both original equations.

The goal of the method of substitution is to reduce a system of two linear equations in two variables to a single equation in one variable. To get it:

1. Find the value of one unknown in either of the given equations.
2. Substitute this value in the other equation.

Solve using substitution: $\left{-2x+y=8\\3x+2y=9$
1. Find the value of y in the first equation y=2x+8
2. Substitute this value in the second equation and solve for x:

3x+2·(2x+8)=9
3x+4x+16=9
7x=9-16
7x=-7
x=-1

To find the y-coordinate, back-substitute the x-value into y=2x+8:

y=2·(-1)+8
y=-2+8
y=-6
The solution is (-1,-6)

Solve using subtitution:

 $\left{-x-3y=-36\\-x+3y=30$ x= y=