Question

3x - 7y = -14\
-3x + 6y = 9\
show your work

Explanation:

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

We have the system of equations:
\[

$$\begin{cases} 3x - 7y = -14 \\ -3x + 6y = 9 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations respectively:
\((3x-7y)+(-3x + 6y)=-14 + 9\)
Simplify the left - hand side: \(3x-7y-3x + 6y=(3x-3x)+(-7y + 6y)=-y\)
Simplify the right - hand side: \(-14 + 9=-5\)
So we get the equation \(-y=-5\)

Step2: Solve for \(y\)

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

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

Let's substitute \(y = 5\) into the first equation \(3x-7y=-14\)
We have \(3x-7\times5=-14\)
First, calculate \(7\times5 = 35\), so the equation becomes \(3x-35=-14\)
Add 35 to both sides of the equation: \(3x-35 + 35=-14 + 35\)
Simplify: \(3x=21\)
Divide both sides by 3: \(x=\frac{21}{3}=7\)

Answer:

The solution of the system of equations is \(x = 7,y = 5\)