Question

linear systems
solving a system of linear equations using elimination with addition
solve the following system of equations.
3x - 8y = 7
-3x + 13y = -17
x =

y =

Explanation:

Step1: Eliminate x by adding equations

Add the two equations \( 3x - 8y = 7 \) and \( -3x + 13y = -17 \) together. The \( 3x \) and \( -3x \) will cancel out.

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Step2: Solve for y

Divide both sides of the equation \( 5y = -10 \) by 5 to find the value of \( y \).

$$ y = \frac{-10}{5} = -2 $$

Step3: Substitute y into one of the original equations to solve for x

We'll use the first equation \( 3x - 8y = 7 \). Substitute \( y = -2 \) into this equation:

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Step4: Solve for x

Subtract 16 from both sides of the equation \( 3x + 16 = 7 \):

$$ 3x = 7 - 16\\ 3x = -9 $$

Then divide both sides by 3:

$$ x = \frac{-9}{3} = -3 $$

Answer:

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