Question

solve by the method of your choice.
$7x - 4y = 4$
$4x + y = 22$

Explanation:

Step1: Solve the second equation for y

From \(4x + y = 22\), we can express \(y\) in terms of \(x\) by subtracting \(4x\) from both sides. So, \(y = 22 - 4x\).

Step2: Substitute y into the first equation

Substitute \(y = 22 - 4x\) into \(7x - 4y = 4\). We get \(7x - 4(22 - 4x) = 4\).

Step3: Simplify and solve for x

First, distribute the -4: \(7x - 88 + 16x = 4\). Then combine like terms: \(23x - 88 = 4\). Add 88 to both sides: \(23x = 92\). Divide both sides by 23: \(x = 4\).

Step4: Substitute x back to find y

Substitute \(x = 4\) into \(y = 22 - 4x\). So, \(y = 22 - 4\times4 = 22 - 16 = 6\).

Answer:

The solution to the system of equations is \(x = 4\) and \(y = 6\), or the ordered pair \((4, 6)\).