Question

elimination with multiplication
question 3 of 10 (1 point) | question attempt: 1 of 3
solve the following system of equations.
$9x - 7y = -1$
$-7x + 3y = 13$
$x = \square$
$y = \square$

Explanation:

Step1: Multiply equations to eliminate a variable

We have the system:

$$
LATEXBLOCK0
$$

Multiply equation (1) by 3 and equation (2) by 7 to make the coefficients of \(y\) opposites:

$$
LATEXBLOCK1
$$

Step2: Add the two new equations

Add \((1')\) and \((2')\) to eliminate \(y\):

$$ 27x - 49x - 21y + 21y = -3 + 91 $$

Simplify:

$$ -22x = 88 $$

Step3: Solve for \(x\)

Divide both sides by \(-22\):

$$ x = \frac{88}{-22} = -4 $$

Step4: Substitute \(x\) into one of the original equations

Substitute \(x = -4\) into equation (1):

$$ 9(-4) - 7y = -1 $$

Simplify:

$$ -36 - 7y = -1 $$

Add 36 to both sides:

$$ -7y = -1 + 36 = 35 $$

Step5: Solve for \(y\)

Divide both sides by \(-7\):

$$ y = \frac{35}{-7} = -5 $$

Answer:

\(x = -4\), \(y = -5\)