Question

find the solution of the system of equations.
-3x - 2y = 36
3x - 5y = 6
answer attempt 1 out of 5
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Explanation:

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

We have the system:
\[

$$\begin{cases} -3x - 2y = 36 \\ 3x - 5y = 6 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations:
\((-3x - 2y)+(3x - 5y)=36 + 6\)
Simplify the left - hand side: \(-3x+3x-2y - 5y=-7y\), and the right - hand side is \(42\). So we get the equation \(-7y = 42\).

Step2: Solve for \(y\)

Divide both sides of the equation \(-7y = 42\) by \(-7\):
\(y=\frac{42}{-7}=-6\)

Step3: Substitute \(y = - 6\) into one of the original equations to solve for \(x\)

We substitute \(y=-6\) into the second equation \(3x-5y = 6\).
So \(3x-5\times(-6)=6\)
Simplify: \(3x + 30=6\)
Subtract \(30\) from both sides: \(3x=6 - 30=-24\)
Divide both sides by \(3\): \(x=\frac{-24}{3}=-8\)

Answer:

\((-8,-6)\)