Question

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solve the system of equations.
$7y + 10x = -11$
$4y - 3x = -15$
$x = \square$
$y = \square$
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Explanation:

Step1: Label the equations

Let
$7y + 10x = -11$ --- (1)
$4y - 3x = -15$ --- (2)

Step2: Eliminate $y$ via scaling

Multiply (1) by 4: $28y + 40x = -44$ --- (3)
Multiply (2) by 7: $28y - 21x = -105$ --- (4)

Step3: Subtract (4) from (3)

$(28y + 40x) - (28y - 21x) = -44 - (-105)$
$61x = 61$

Step4: Solve for $x$

$x = \frac{61}{61} = 1$

Step5: Substitute $x=1$ into (2)

$4y - 3(1) = -15$
$4y - 3 = -15$

Step6: Solve for $y$

$4y = -15 + 3 = -12$
$y = \frac{-12}{4} = -3$

Answer:

$x = 1$
$y = -3$