# Solving a System of Equations Using Elimination

Learn how to solve a system of equations using elimination.

To solve a system of equations using elimination, you start by adding them together to form one equation. This is done by combining like-terms.

However, you have to set the equations so that the a variable cancels out when you add the 2 equations together.

This can be done by multiplying each equation by a common factor, so that a variable in both equations can be cancelled out.

You should only be left with one variable, and real numbers.

After that, you simplify to find what that variable is equal to.

You then plug your answer into one of the original equations to find the other variable, and to find the coordinate.

To check your answer, plug both x and y-values into an original equation to see if it holds true.

Example:

$4x + 2y = 8$
$\underline{-2x - 2y = 6}$
$2x = 14$
$x = 7$
$\downarrow$
$4(7) + 2y = 8$
$28 + 2y = 8$
$20 = -2y$
$y = -10$

So the coordinates for the point of intersection would be (7,-10).

Check:

$-2x - 2y = 6$
$-2(7) - 2(10) = 6$
$-14 + 20 = 6$
$6 = 6$

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Used by students across the country. Pre-Algebra, Algebra I, Geometry, & Algebra II