SOLUTION: How do you solve for x and y, and then graph these equations? 8x + 2y = 7 3x - 4y = 5

Algebra ->  Graphs -> SOLUTION: How do you solve for x and y, and then graph these equations? 8x + 2y = 7 3x - 4y = 5      Log On


   



Question 342318: How do you solve for x and y, and then graph these equations?
8x + 2y = 7
3x - 4y = 5

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply the first equation by 2 and add them,
16x%2B4y%2B3x-4y=14%2B5
19x=19
highlight%28x=1%29
Then use either equation to solve for y
3%281%29-4y=5
-4y=2
highlight%28y=-1%2F2%29
.
.
.
Convert both equations to slope intercept form, y=mx%2Bb.
8x+%2B+2y+=+7
2y=-8x%2B7
y=-4x%2B7%2F2
Plot the y-intercept (0,7%2F2).
Then use the slope to calculate another point on the line.
Slope is change in y over change in x.
If x changes by 2, then y will change by 2%28-4%29=-8,
Another point on the line would be,
x=0%2B2=2
y=7%2F2%2B2%28-4%29=-9%2F2
(2,-9%2F2)
.
.
.

.
.
.
3x+-+4y+=+5
-4y=-3x%2B5
y=%283%2F4%29x-5%2F4
.
.
.
Plot the y-intercept (0,-5%2F4).
Then use the slope to calculate another point on the line.
If x changes by 4, then y will change by 4%283%2F4%29=3,
Another point on the line would be,
x=0%2B4=4
y=-5%2F4%2B3=7%2F4
(4,7%2F4)
.
.
.

.
.
.
Note the intersection of the lines occurs at (1,-1%2F2) as previously determined algebraically.