Question

1. how many solutions does the system of equations below have?

y = -9x + 2
y = -9x - \frac{7}{8}
no solution
one solution
infinitely many solutions
7 how many solutions does the system of equations below have?
2x - y = 8
-18x - 17y = 13
no solution
one solution
infinitely many solutions

Explanation:

For Question 6:

Step1: Compare slopes of lines

Both equations are in $y=mx+b$ form. For $y=-9x+2$, slope $m_1=-9$. For $y=-9x-\frac{7}{8}$, slope $m_2=-9$.

Step2: Compare y-intercepts

Y-intercept $b_1=2$, $b_2=-\frac{7}{8}$. Since $m_1=m_2$ but $b_1
eq b_2$, lines are parallel and never intersect.

Step1: Rewrite equations to slope-intercept

First equation: $2x - y = 8 \implies y=2x-8$, slope $m_1=2$.
Second equation: $-18x -17y=13 \implies -17y=18x+13 \implies y=-\frac{18}{17}x-\frac{13}{17}$, slope $m_2=-\frac{18}{17}$.

Step2: Analyze slope relationship

Since $m_1
eq m_2$, the two lines intersect at exactly one point.

Answer:

no solution

---

For Question 7: