Question

how many solutions does the system of equations have?
y = -\frac{1}{2}x + 11
2x + 2y = 20
a 1 solution
b no solution
c infinitely many solutions
d cannot be determined

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

Start with $7x + 2y = 20$. Isolate $y$:
$2y = -7x + 20$
$y = -\frac{7}{2}x + 10$

Step2: Compare slopes of both lines

First line: $y = -\frac{7}{3}x + 11$, slope $m_1 = -\frac{7}{3}$
Second line: $y = -\frac{7}{2}x + 10$, slope $m_2 = -\frac{7}{2}$
Since $-\frac{7}{3}
eq -\frac{7}{2}$, the lines are not parallel.

Step3: Determine number of solutions

Non-parallel lines intersect at exactly one point, so the system has one solution.

Answer:

A. 1 solution