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System of equations
Solving systems of equations using elimination

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

The goal of the method of substitution is to obtain opposite coefficients for one of the variables so that adding the two equations eliminates this variable.

1. Multiply the given equations by such numbers as will make the coefficients of one unknown in the resulting equation numerically equal.
2. If the signs of the equal coefficients are unlike, add the resulting equations; if like, subtract them.

Solve using elimination: $\left{4x-3y=-13\\5x+2y=1$
1. Multiply the first equation by -5 and the second equation by 4.

$\left{-20x+15y=65\\20x+8y=4$

2. Add the resulting equations and solve for y:
23y=69
y=3

To find the x-coordinate, back-substitute the x-value into the firts equation
4x-3·3=-13
4x-9=-13
4x=-13+9
4x=-4
x=-1
The solution is (-1,3)
:

Solve using elimination:

 $\left{-2x-4y=-16\\5x+5y=20$ x= y=