Question

solve the system of equations $-x + y = 5$ and $7x - 6y = -25$ by combining the equations.
$\square\

$$\begin{cases}(-x + y = 5)\\\\(7x - 6y = -25)\\end{cases}$$

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$$\begin{align*}-x + y &= 5\\\\7x - 6y &= -25\\\\\\hline\\square x+\\square y&=\\square\\end{align*}$$

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try
answer attempt 1 out of 2
you must answer all questions above in order to submit.

Explanation:

Step1: Eliminate x, scale first equation

Multiply first equation by 7: $7(-x + y) = 7(5)$ $\implies -7x + 7y = 35$

Step2: Add scaled equation to second

Add to $7x - 6y = -25$:
$$(-7x + 7y) + (7x - 6y) = 35 + (-25)$$

Step3: Simplify to find y

$(-7x+7x)+(7y-6y)=10$ $\implies y=10$

Step4: Substitute y to find x

Plug $y=10$ into $-x + y = 5$:
$-x + 10 = 5$ $\implies -x = 5 - 10$ $\implies -x = -5$ $\implies x=5$

For the blank scaling coefficient and combined equation:

Step1: Set scaling factor for x elimination

Choose scaling factor 7 for first equation: $\boldsymbol{7}(-x + y = 5)$

Step2: Combine the two equations

Add scaled first equation to second:

$$\begin{align*} -7x + 7y &= 35 \\ + \quad 7x - 6y &= -25 \\ \hline \boldsymbol{0}x + \boldsymbol{1}y &= \boldsymbol{10} \end{align*}$$

Answer:

Scaling coefficient: $7$
Combined equation: $0x + 1y = 10$
Solution to the system: $x=5$, $y=10$