Question

-6x - 2y = 8
-2x + 5y = 14

Explanation:

Step1: Label the equations

Let \(-6x - 2y = 8\) be Equation (1) and \(-2x + 5y = 14\) be Equation (2).

Step2: Eliminate \(x\)

Multiply Equation (2) by 3: \(3\times(-2x + 5y)=3\times14\), which gives \(-6x + 15y = 42\) (let's call this Equation (3)).

Step3: Subtract Equation (1) from Equation (3)

\((-6x + 15y)-(-6x - 2y)=42 - 8\)
Simplify: \(-6x + 15y + 6x + 2y = 34\)
Combine like terms: \(17y = 34\)

Step4: Solve for \(y\)

Divide both sides by 17: \(y=\frac{34}{17}=2\)

Step5: Substitute \(y = 2\) into Equation (2)

\(-2x + 5\times2 = 14\)
Simplify: \(-2x + 10 = 14\)

Step6: Solve for \(x\)

Subtract 10 from both sides: \(-2x = 14 - 10 = 4\)
Divide by -2: \(x=\frac{4}{-2}=-2\)

Answer:

The solution is \(x = -2\), \(y = 2\)