Question

solve.
-6x - 7y = -9
5x + 7y = 4
(\boxed{}, \boxed{})
submit

Explanation:

Step1: Add the two equations to eliminate \( y \)

We have the system of equations:
\[

$$\begin{cases} -6x - 7y = -9 \\ 5x + 7y = 4 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations respectively:
\((-6x - 7y)+(5x + 7y)=-9 + 4\)
Simplify the left - hand side: \(-6x-7y + 5x + 7y=-x\), and the right - hand side: \(-9 + 4=-5\). So we get the equation \(-x=-5\).

Step2: Solve for \( x \)

From \(-x=-5\), multiply both sides by \(- 1\) to get \(x = 5\).

Step3: Substitute \( x = 5 \) into one of the original equations to solve for \( y \)

Let's substitute \(x = 5\) into the second equation \(5x+7y = 4\).
We have \(5\times5+7y=4\), which simplifies to \(25 + 7y=4\).
Subtract 25 from both sides: \(7y=4 - 25=-21\).
Divide both sides by 7: \(y=\frac{-21}{7}=-3\).

Answer:

\((5,-3)\)