Step 1) Solve the first equation for y:
2x + y = 5
2x - color(red)(2x) + y = 5 - color(red)(2x)
0 + y = 5 - 2x
y = 5 - 2x
Step 2) Substitute 5 - 2x for y in the second equation and solve for x:
2x - 5y = 1 becomes:
2x - 5(5 - 2x) = 1
2x - 25 + 10x = 1
12x - 25 = 1
12x - 25 + color(red)(25) = 1 + color(red)(25)
12x - 0 = 26
12x = 26
(12x)/color(red)(12) = 26/color(red)(12)
(color(red)(cancel(color(black)(12)))x)/cancel(color(red)(12)) = 13/6
x = 13/6
Step 3) Substitute 13/6 for x in the solution to the first equation at the end of Step 1 and calculate y:
y = 5 - 2x becomes:
y = 5 - (2 xx 13/6)
y = 5 - 26/6
y = (6/6 xx 5) - 26/6
y = 30/6 - 26/6
y = 4/6
y = 2/3
The solution is x = 13/6 and y = 2/3 or (13/6, 2/3)
