Question

Solve the system. Show your work using Graphing OR Substitution OR Elimination.
Check your answer by showing your solution works in both original equations.

y = 2x -6
y = -½ x +4

Answer 1

The solution is x = 4 and y = 2

Explanation:

We have the following system of two linear equations in two variables:

$\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}y=2x-6\\y=-\frac{1}{2}x+4\end{array}\right.$

Subtract (2) from (1):

$\begin{array}{c}(1)\\(2)\end{array}\left\{ \begin{array}{c}y=2x-6\\ -\left(y=-\frac{1}{2}x+4\right)\end{array}\right \\ \\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ \\ y-y=2x-6-(-\frac{1}{2}x+4) \\ \\ 0=2x-6+\frac{1}{2}x-4 \\ \\ Combine \ like \ terms: \\ \\ 2x+\frac{1}{2}x-6-4=0 \\ \\ 2.5x-10=0 \\ \\ 2.5x=10 \\ \\ x=\frac{10}{2.5} \\ \\ x=4$

Substituting the x-value into (1):

$y=2(4)-6 \\ \\ y=8-6 \\ \\ y=2$

So the solution to this system is:

$\boxed{x=4 \ and \ y=2}$

Learn more:

Methods for solving systems of linear equations:

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