Step 1) Solve the first equation for yy:
5x + y = 25x+y=2
-color(red)(5x) + 5x + y = -color(red)(5x) + 2−5x+5x+y=−5x+2
0 + y = -5x + 20+y=−5x+2
y = -5x + 2y=−5x+2
Step 2) Substitute -5x + 2−5x+2 for yy in the second equation and solve for xx:
13x - 5y = -213x−5y=−2 becomes:
13x - 5(-5x + 2) = -213x−5(−5x+2)=−2
13x - (5 xx -5x) - (5 xx 2) = -213x−(5×−5x)−(5×2)=−2
13x + 25x - 10 = -213x+25x−10=−2
38x - 10 = -238x−10=−2
38x - 10 + color(red)(10) = -2 + color(red)(10)38x−10+10=−2+10
38x - 0 = 838x−0=8
38x = 838x=8
(38x)/color(red)(38) = 8/color(red)(38)38x38=838
(color(red)(cancel(color(black)(38)))x)/cancel(color(red)(38)) = (2 xx 4)/color(red)(2 xx 19)
x = (color(red)(cancel(color(black)(2))) xx 4)/color(red)(cancel(2) xx 19)
x = 4/19
Step 3) Substitute 4/19 for x in the solution to the first equation at the end of Step 1 and calculate y:
y = -5x + 2 becomes:
y = (-5 xx 4/19) + 2
y = -20/19 + 2
y = -20/19 + (19/19 xx 2)
y = -20/19 + 38/19
y = 18/19
The solution is: x = 4/19 and y = 18/19 or (4/19, 18/19)
