Question

solve the following system of equations.
3x - 2y = -3
-6x + 7y = 6
x =

y =

Explanation:

Step1: Multiply first equation by 2

To eliminate \(x\), multiply the first equation \(3x - 2y=-3\) by 2. We get \(2\times(3x - 2y)=2\times(-3)\), which simplifies to \(6x-4y = - 6\).

Step2: Add to second equation

Now add the new equation \(6x - 4y=-6\) to the second equation \(-6x + 7y=6\). So, \((6x-4y)+(-6x + 7y)=-6 + 6\). Simplifying the left - hand side: \(6x-6x-4y + 7y=3y\), and the right - hand side: \(0\). So we have \(3y=0\), which gives \(y = 0\) when we divide both sides by 3.

Step3: Substitute y into first equation

Substitute \(y = 0\) into the first equation \(3x-2y=-3\). We get \(3x-2\times0=-3\), which simplifies to \(3x=-3\).

Step4: Solve for x

Divide both sides of \(3x=-3\) by 3. So \(x=\frac{-3}{3}=-1\).

Answer:

\(x=-1\)
\(y = 0\)