Question

3, consider the following equations; -2x + 4y = 8 4x - 2y = 8

Explanation:

Step1: Solve the first equation for y

Starting with \(-2x + 4y = 8\), add \(2x\) to both sides: \(4y = 2x + 8\). Then divide by 4: \(y=\frac{2x + 8}{4}=\frac{1}{2}x + 2\).

Step2: Solve the second equation for y

Starting with \(4x - 2y = 8\), subtract \(4x\) from both sides: \(-2y=-4x + 8\). Then divide by -2: \(y = 2x-4\).

Step3: Set the two equations equal to find x

Set \(\frac{1}{2}x + 2=2x - 4\). Subtract \(\frac{1}{2}x\) from both sides: \(2=\frac{3}{2}x - 4\). Add 4 to both sides: \(6=\frac{3}{2}x\). Multiply both sides by \(\frac{2}{3}\): \(x = 4\).

Step4: Substitute x back to find y

Substitute \(x = 4\) into \(y = 2x-4\): \(y=2(4)-4 = 4\). So the solution is \((4,4)\).

Answer:

The solution to the system of equations is \(x = 4\), \(y = 4\) (or the ordered pair \((4,4)\)).