How many solutions does the system of equations below have? y = x + 6 y = x + 9/4 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Compare Equations: Compare the two equations to see if they are the same or if they intersect at a point. The equations are y = x + 6 and y = x + 9/4. Compare Slopes: Since both equations are in the form y = mx + b, where m is the slope and b is the y-intercept, we can compare their slopes and intercepts. The slopes (m) of both equations are 1, which means they are parallel lines. Check Y-Intercepts: Check the y-intercepts of both equations. The first equation has a y-intercept of 6, and the second equation has a y-intercept of 9/4. Since the y-intercepts are different, the lines do not intersect and are not the same line.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How many solutions does the system of equations below have? $\newline$ $y = x + 6$ $\newline$ $y = x + \frac{9}{4}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

View step-by-step help

Home

Math Problems

Precalculus

Solve trigonometric equations

Full solution

Q. How many solutions does the system of equations below have?

\newline

y = x + 6

\newline

y = x + \frac{9}{4}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Compare Equations: Compare the two equations to see if they are the same or if they intersect at a point. The equations are $y = x + 6$ and $y = x + \frac{9}{4}$ .
Compare Slopes: Since both equations are in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept, we can compare their slopes and intercepts. The slopes ( $m$ ) of both equations are $1$ , which means they are parallel lines.
Check Y-Intercepts: Check the y-intercepts of both equations. The first equation has a y-intercept of $6$ , and the second equation has a y-intercept of $\frac{9}{4}$ . Since the y-intercepts are different, the lines do not intersect and are not the same line.