Question

find the solution of the system of equations.
$5x + 10y = -5$
$-5x - y = 32$

Explanation:

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

The system of equations is:

$$
LATEXBLOCK0
$$

Adding the left - hand sides and the right - hand sides of the two equations:
\((5x + 10y)+(-5x - y)=-5 + 32\)
Simplify the left - hand side: \(5x-5x + 10y-y=9y\)
Simplify the right - hand side: \(27\)
So we get the equation \(9y=27\)

Step2: Solve for \(y\)

From \(9y = 27\), divide both sides by \(9\):
\(y=\frac{27}{9}=3\)

Step3: Substitute \(y = 3\) into one of the original equations to solve for \(x\)

We substitute \(y = 3\) into the first equation \(5x+10y=-5\)
\(5x+10\times3=-5\)
\(5x + 30=-5\)
Subtract \(30\) from both sides: \(5x=-5 - 30=-35\)
Divide both sides by \(5\): \(x=\frac{-35}{5}=-7\)

Answer:

The solution of the system of equations is \(x=-7\), \(y = 3\)