Step 1) Solve the first equation for yy:
2x + y = 52x+y=5
2x - color(red)(2x) + y = 5 - color(red)(2x)2x−2x+y=5−2x
0 + y = 5 - 2x0+y=5−2x
y = 5 - 2xy=5−2x
Step 2) Substitute 5 - 2x5−2x for yy in the second equation and solve for xx:
2x - 5y = 12x−5y=1 becomes:
2x - 5(5 - 2x) = 12x−5(5−2x)=1
2x - 25 + 10x = 12x−25+10x=1
12x - 25 = 112x−25=1
12x - 25 + color(red)(25) = 1 + color(red)(25)12x−25+25=1+25
12x - 0 = 2612x−0=26
12x = 2612x=26
(12x)/color(red)(12) = 26/color(red)(12)12x12=2612
(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)
