solve the system by graphing

Question

y=x−1

y=−21​x+2

Answer 1

These equations are both in slope-y-intercept form. So to graph the first equation, we start at the y-intercept, (0,-1). Then, because the slope is 1, we can add a few additional points going up by 1 for every unit to the right (or down by 1 for every unit to the left). So we add (-1,-2), (1,0), and (2,1) to the graph. Then we can draw a line connecting all these points.

For the second equation, we do the same thing. Start at the y-intercept, (0,2). Then, because the slope is -21, we can add a few additional points going down 21 for every unit to the right. So we add (-1,23), (1,-19), and (2,-40) to the graph. Then we can draw a line connecting all these points. We find the point of intersection at (3/22,-19/22).

(In all honesty, I don't know that by looking at a graph. I solve algebraically. The point of intersection is when y for the first and y for the second are equal. So we set up

x-1=-21x+2

x-1+21x+1=-21x+2+21x+1 Add 21x to both sides and add 1 to both sides.

22x=3 Combine like terms

22x/22=3/22 Divide both sides by 22

x=3/22

Then substitute back into either equation. The first one is simpler:

y=3/22-1

y=3/22-22/22 Find a common denominator

y=-19/22

To check, we verify that the second equation gives the same answer:

y=-21⋅3/22+2

y=-63/22+2

y=-63/22+44/22 Find a common denominator

y=-19/22

Since we got the same answer, we know we are correct.)