Question

analyzing a system of equations with no solution
consider this system of linear equations
y = -3x + 5
y = mx + b
which values of m and b will create a system of linear
equations with no solution?
○ m = -3 and b = -3
○ m = 5 and b = -3
○ m = 3 and b = 5
○ m = -3 and b = 5

Explanation:

Step1: Recall no-solution condition

A system of linear equations $y = a_1x + b_1$ and $y = a_2x + b_2$ has no solution if $a_1 = a_2$ (same slope, parallel lines) and $b_1
eq b_2$ (different y-intercepts, distinct lines).

Step2: Match to given equation

For $y = -3x + 5$, we need $m = -3$ (same slope) and $b
eq 5$ (different intercept).

Step3: Select valid option

From choices, $m=-3$ and $b=-3$ satisfies both conditions.

Answer:

A. $m = -3$ and $b = -3$