Question

What is the solution to the linear system of equations?
y = 3x + 1
y = –x + 5











A.
(2, 7)







B.
(0, 5)







C.
(1, 4)







D.
The system has no solution

Answer 1

So your step by step method to solving questions of this kind,

Step 1) you put the equations into their general, slope-intercept form, which is usually\[y=mx+b\]where m is the slope of the line, and b is your y-intercept (the value of Y when X=0)

Step 2) compare the slopes of the lines you have, if the slopes are equal, then you need to check the value of B, if those are the same, then the lines are the same and therefore have infinitely many solutions, if the lines have different B values, then there are no solutions, if the slopes are different, move to step 3

Step 3) if you have the equations in the form Y=mX + B, set them equal to eachother and solve for the X-value

Step 4) Plug that X-value that you got from step 3 into the original equations to get your Y-value, check both equations, you should get the same point for both, if you do, that's your single point of intersection, if they are different, you did something wrong in a previous step.

I really hope this helps you solve all of your future questions of this kind :)

Answer 2

Thanks so much embyoy!

Answer 3

C.

Answer 4

y = 3x + 1 and y = -x + 5
this is the same y therefore 3x + 1 = -x + 5
solve for x 4x = 4 so x = 1
using this value in either expression for y find y
(1, 4) = C