Question

Difficulty: EasySolving Systems of Linear Equations

Given the system of equations below, what is the value of $x$ ?

3x + 2y = 16

x - 2y = 0

Answer: 4 / x=4 / x = 4 / four

Because the coefficients of

y

in the two equations are opposites (

+2

and

-2

), the fastest approach is the elimination method. Adding the equations top-to-bottom yields

(3x + x) + (2y - 2y) = 16 + 0

, which simplifies directly to

4x = 16

. Dividing both sides by

4

gives

x = 4

Add the two equations together.

4x = 16

The

2y

and

-2y

terms are opposites, so adding the equations eliminates the

y

variable entirely.

Divide both sides of the resulting equation by 4.

x = 4

This isolates the variable

x

to find its exact numerical value.

Solving systems of linear equations using the elimination method.

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