Question

solve the following system of equations.
$x + 7y = 17$
$-x - 9y = -21$

Explanation:

Step1: Add the two equations

We have the system:

$$
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$$

Adding the two equations together: \((x + 7y)+(-x - 9y)=17+(-21)\)
Simplify the left side: \(x - x+7y - 9y=-2y\)
Simplify the right side: \(17 - 21=-4\)
So we get \(-2y=-4\)

Step2: Solve for y

Divide both sides of \(-2y = - 4\) by \(-2\): \(y=\frac{-4}{-2}=2\)

Step3: Substitute y into the first equation

Substitute \(y = 2\) into \(x+7y = 17\): \(x+7\times2=17\)
Simplify: \(x + 14=17\)
Subtract 14 from both sides: \(x=17 - 14 = 3\)

Answer:

\(x = 3\), \(y = 2\)