Question

On your own paper, rewrite these equations in slope intercept form showing all steps, y=mx+b
. Determine the number of solutions.

−x+3y=21


5x−4y=−44

(1 point)
−x+3y=21
written in slope intercept form is y=
x+


5x−4y=−44
written in slope intercept form is y=

x+


Question 2
What is the number of solutions to this system?(1 point)
Responses

One Solution
One Solution

No Solution
No Solution

Infinitely Many Solutions
Infinitely Many Solutions

Unable to determine given the available information

Answer 1

Solve each equation for y (slope-intercept form y = mx + b):

1) −x + 3y = 21
- Add x to both sides: 3y = x + 21
- Divide by 3: y = (1/3)x + 7

So y = (1/3)x + 7.

2) 5x − 4y = −44
- Subtract 5x from both sides: −4y = −5x − 44
- Divide by −4: y = (−5/−4)x + (−44/−4) = (5/4)x + 11

So y = (5/4)x + 11.

Number of solutions for the system:
The slopes are 1/3 and 5/4, which are different, so the lines intersect at exactly one point.

Answer: One Solution.