Step 1) Solve each equation for 7y7y:
Equation 1:
2x + 7y = 12x+7y=1
-color(red)(2x) + 2x + 7y = -color(red)(2x) + 1−2x+2x+7y=−2x+1
0 + 7y = -2x + 10+7y=−2x+1
7y = -2x + 17y=−2x+1
Equation 2:
5x - 7y = 125x−7y=12
-color(red)(5x) + 5x - 7y = -color(red)(5x) + 12−5x+5x−7y=−5x+12
0 - 7y = -5x + 120−7y=−5x+12
-7y = -5x + 12−7y=−5x+12
color(red)(-1) xx -7y = color(red)(-1)(-5x + 12)−1×−7y=−1(−5x+12)
7y = 5x - 127y=5x−12
Step 2) Because the left side of each equation is 7y7y we can equate the right side of each equation and solve for xx:
-2x + 1 = 5x - 12−2x+1=5x−12
color(red)(2x) - 2x + 1 + color(blue)(12) = color(red)(2x) + 5x - 12 + color(blue)(12)2x−2x+1+12=2x+5x−12+12
0 + 13 = (color(red)(2) + 5)x - 00+13=(2+5)x−0
13 = 7x13=7x
13/color(red)(7) = (7x)/color(red)(7)137=7x7
13/7 = (color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7))
13/7 = x
x = 13/7
*Step 3) Substitute 13/7 for x in the solution to either equation in Step 1 and calculate y:
7y = -2x + 1 becomes:
7y = (-2 xx 13/7) + 1
7y = -26/7 + 1
7y = -26/7 + (7/7 xx 1)
7y = -26/7 + 7/7
7y = -19/7
(7y)/color(red)(7) = (-19/7)/color(red)(7)
(color(red)(cancel(color(black)(7)))y)/cancel(color(red)(7)) = -19/49
y = -19/49
The Solution Is: x = 13/7 and y = -19/49 or (13/7, -19/49)
