Question

solve the system of equations $-2x - y = -5$ and $3x - 4y = -42$ by combining the equations.
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$$\begin{pmatrix}-2x & -y & = -5\\\\3x & -4y & = -42\\end{pmatrix}$$

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$$\begin{align*}-2x & - y & = & -5\\\\3x & - 4y & = & -42\\\\\\hline 0\\ x + 0\\ y & = & \\end{align*}$$

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answer attempt 1 out of 3
you must answer all questions above in order to submit.

Explanation:

Step1: Eliminate $x$ via scaling

Multiply first equation by 3: $3(-2x - y) = 3(-5) \implies -6x - 3y = -15$
Multiply second equation by 2: $2(3x - 4y) = 2(-42) \implies 6x - 8y = -84$

Step2: Add scaled equations

Add the two new equations:
$$(-6x - 3y) + (6x - 8y) = -15 + (-84)$$
$$0x - 11y = -99$$

Step3: Solve for $y$

Divide both sides by $-11$:
$$y = \frac{-99}{-11} = 9$$

Step4: Substitute $y=9$ to find $x$

Plug $y=9$ into $-2x - y = -5$:
$$-2x - 9 = -5$$
$$-2x = -5 + 9 = 4$$
$$x = \frac{4}{-2} = -2$$

Answer:

$x=-2$, $y=9$

For the intermediate combination step shown: $0x + 0y$ is not the correct combination; the valid combination to eliminate $x$ gives $0x - 11y = -99$, and the final solution is $x=-2$, $y=9$.