Question

find the solution of the system of equations.

$5x + y = -19$
$5x - 4y = -24$

answer
attempt 1 out of 2
$\left(\square, \square\
ight)$ submit answer

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} 5x + y = -19 \\ 5x - 4y = -24 \end{cases}$$

Subtract the second equation from the first to eliminate \(x\):
$$(5x + y) - (5x - 4y) = -19 - (-24)$$
Simplify the left - hand side: \(5x + y - 5x + 4y=5y\)
Simplify the right - hand side: \(-19 + 24 = 5\)
So we get the equation \(5y=5\)

Step2: Solve for y

Divide both sides of \(5y = 5\) by 5:
\(y=\frac{5}{5}=1\)

Step3: Substitute y into one of the original equations

Substitute \(y = 1\) into the first equation \(5x + y=-19\), we have:
\(5x+1=-19\)
Subtract 1 from both sides: \(5x=-19 - 1=-20\)
Divide both sides by 5: \(x=\frac{-20}{5}=-4\)

Answer:

\((-4,1)\)