Question

1. solve using elimination

$8x - 4y = 0$
$7x + 8y = 23$

Explanation:

Step1: Eliminate y by multiplying first equation

Multiply the first equation \(8x - 4y = 0\) by 2 to make the coefficients of y opposite. So we get \(16x - 8y = 0\).

Step2: Add the two equations

Add the new first equation \(16x - 8y = 0\) and the second equation \(7x + 8y = 23\). This gives \((16x + 7x)+(-8y + 8y)=0 + 23\), which simplifies to \(23x=23\).

Step3: Solve for x

Divide both sides of \(23x = 23\) by 23. So \(x=\frac{23}{23}=1\).

Step4: Substitute x into first equation

Substitute \(x = 1\) into the original first equation \(8x - 4y = 0\). We get \(8(1)-4y = 0\), which is \(8 - 4y = 0\).

Step5: Solve for y

Subtract 8 from both sides: \(-4y=-8\). Then divide by -4: \(y=\frac{-8}{-4}=2\).

Answer:

The solution to the system is \(x = 1\) and \(y = 2\) (or as an ordered pair \((1, 2)\)).