Question

find the solution of the system of equations.\\(-4x + 3y = -21\\)\\(-2x - 3y = 3\\)\\(\text{answer attempt 1 out of 5}\\)\\((\square, \square)\\)\\(\text{submit answer}\\)

Explanation:

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

We have the system:
\[

$$\begin{cases} -4x + 3y = -21 \\ -2x - 3y = 3 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations:
\((-4x + 3y)+(-2x - 3y)=-21 + 3\)
Simplify the left - hand side: \(-4x-2x+3y - 3y=-6x\)
Simplify the right - hand side: \(-18\)
So we get the equation \(-6x=-18\)

Step2: Solve for \( x \)

Divide both sides of the equation \(-6x=-18\) by \(-6\):
\(x=\frac{-18}{-6}=3\)

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

Let's substitute \( x = 3 \) into the second equation \(-2x-3y = 3\)
We have \(-2\times3-3y=3\)
Simplify the left - hand side: \(-6-3y=3\)
Add 6 to both sides: \(-3y=3 + 6=9\)
Divide both sides by \(-3\): \(y=\frac{9}{-3}=-3\)

Answer:

\((3,-3)\)