Question

lesson 3 one solution, no solution, or many solutions -3x + y = 7 y = 3x - 2

Explanation:

Step1: Analyze the slopes of the two lines

First, rewrite the equations in slope - intercept form ($y = mx + b$, where $m$ is the slope and $b$ is the y - intercept).
For the equation $-3x + y=7$, we can rewrite it as $y = 3x+7$. The slope of this line, $m_1$, is 3.
For the equation $y = 3x - 2$, the slope of this line, $m_2$, is 3.

Step2: Analyze the y - intercepts

For the line $y = 3x + 7$, the y - intercept $b_1=7$.
For the line $y = 3x - 2$, the y - intercept $b_2=- 2$.

Step3: Determine the relationship between the lines

Since the slopes of the two lines are equal ($m_1=m_2 = 3$) and the y - intercepts are different ($b_1
eq b_2$), the two lines are parallel. Parallel lines in a system of linear equations have no solution because they never intersect.

Answer:

The system of linear equations has no solution.