Question

same coefficients
exact solution to the system: 4x + 2y = 12
4x + 8y = -24

Explanation:

Step1: Subtract the two equations

We have the system:

$$\begin{cases} 4x + 2y = 12 \\ 4x + 8y = -24 \end{cases}$$

Subtract the first equation from the second equation to eliminate \(x\):
\((4x + 8y) - (4x + 2y) = -24 - 12\)
Simplify the left - hand side: \(4x+8y - 4x - 2y=6y\)
Simplify the right - hand side: \(-36\)
So we get the equation \(6y=-36\)

Step2: Solve for y

Divide both sides of the equation \(6y = - 36\) by 6:
\(y=\frac{-36}{6}=-6\)

Step3: Substitute y into one of the original equations to solve for x

Substitute \(y = - 6\) into the first equation \(4x+2y = 12\):
\(4x+2\times(-6)=12\)
Simplify: \(4x-12 = 12\)
Add 12 to both sides: \(4x=12 + 12=24\)
Divide both sides by 4: \(x=\frac{24}{4}=6\)

Answer:

The solution to the system of equations is \(x = 6\) and \(y=-6\) (or in ordered pair form \((6,-6)\))