Question

mathematical connections solve a system of linear equations to find the values of x and y. the linear equations are 4x + 2x + 12 = 180 and 2x + y + 6 = 180. the solutions are x = 28 and y = 58

Explanation:

Step1: Set up equations

In a trapezoid, consecutive angles between the parallel sides are supplementary.
So, \(4x+(y + 6)=180\) (equation 1) and \(2y+(2x + 12)=180\) (equation 2).
From equation 2: \(2y+2x+12 = 180\), simplify to \(y+x=84\), then \(y=84 - x\).

Step2: Substitute \(y = 84 - x\) into equation 1

Substitute \(y\) into \(4x+(y + 6)=180\):
\(4x+(84 - x+6)=180\)
\(4x - x+90=180\)
\(3x=180 - 90\)
\(3x=90\)
\(x = 30\)

Step3: Find \(y\)

Substitute \(x = 30\) into \(y=84 - x\)
\(y=84-30\)
\(y = 54\)

Answer:

\(x = 30\) and \(y = 54\)