Question

practice determining the number of solutions to a system of linear equations▶ study the example showing how to determine the number of solutions to a system of linear equations. then solve problems 1-7.examplehow many solutions does each system of equations have?a.b. $y = 7x + 3LXB0y = mx + 1$3 find a value for $b$ that will give you a system of equations with no solution.$y = 6x + 1$$y = 6x + b$4 draw a line in each coordinate plane so that the lines represent a system of equations with the given number of solutions.a. no solutionb. exactly one solutionc. infinitely many solutions

Explanation:

Step1: Identify intersection point

The two lines in the example graph cross at $(-3, 1)$.

Step2: Define unique solution condition

For $y=6x+1$ and $y=mx+1$, unique solution requires $m
eq 6$. Choose $m=5$.

Step3: Define no solution condition

For $y=6x+1$ and $y=6x+b$, no solution requires $b
eq 1$. Choose $b=-1$.

Step4: Draw lines for solution types

a. No solution: Draw a line parallel to the given line (same slope, different y-intercept).
b. Exactly one solution: Draw a line with a different slope that intersects the given line at one point.
c. Infinitely many solutions: Draw a line identical to the given line (same slope and y-intercept).

Answer:

1. $(-3, 1)$
2. $m=5$ (any value except 6 is valid)
3. $b=-1$ (any value except 1 is valid)
4. a. (Draw a line parallel to the given line, e.g., $y = -x + 1$)

b. (Draw a line with a different slope, e.g., $y = 2x$)
c. (Draw the exact same line as the given one, $y = -x$)