Question

resuelve el sistema por eliminación.
solve the system with the elimination method:
\

$$\begin{cases}-10x + 5y = -65\\\\x - 4y = 31\\end{cases}$$

answer: $(x, y) = (\boxed{\quad}, \boxed{\quad})$
enter your answers as integers or as reduced fraction(s) in the form a/b.
question help: \video
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Explanation:

Step1: Multiply the second equation

To eliminate \(x\), multiply the second equation \(x - 4y = 31\) by \(10\) to get \(10x - 40y = 310\).

Step2: Add the two equations

Add the first equation \(-10x + 5y = -65\) and the new second equation \(10x - 40y = 310\):

$$
LATEXBLOCK0
$$

Step3: Solve for \(y\)

Divide both sides of \(-35y = 245\) by \(-35\): \(y=\frac{245}{-35}=-7\).

Step4: Substitute \(y\) into an equation

Substitute \(y = -7\) into the second original equation \(x - 4y = 31\): \(x-4\times(-7)=31\), which simplifies to \(x + 28 = 31\).

Step5: Solve for \(x\)

Subtract \(28\) from both sides: \(x=31 - 28 = 3\).

Answer:

\((3, -7)\)