Step 1) Solve the first equation for xx:
x - 3y = -1x−3y=−1
x - 3y + color(red)(3y) = -1 + color(red)(3y)x−3y+3y=−1+3y
x - 0 = -1 + 3yx−0=−1+3y
x = -1 + 3yx=−1+3y
Step 2) Substitute -1 + 3y−1+3y for xx in the second equation and solve for yy:
7x + 15y = 327x+15y=32 becomes:
7(-1 + 3y) + 15y = 327(−1+3y)+15y=32
(7 * -1) + (7 * 3y) + 15y = 32(7⋅−1)+(7⋅3y)+15y=32
-7 + 21y + 15y = 32−7+21y+15y=32
-7 + (21 + 15)y = 32−7+(21+15)y=32
-7 + 36y = 32−7+36y=32
color(red)(7) - 7 + 36y = color(red)(7) + 327−7+36y=7+32
0 + 36y = 390+36y=39
36y = 3936y=39
(36y)/color(red)(36) = 39/color(red)(36)36y36=3936
(color(red)(cancel(color(black)(36)))y)/cancel(color(red)(36)) = (13 xx 3)/color(red)(12 xx 3)
y = (13 xx color(red)(cancel(color(black)(3))))/color(red)(12 xx color(black)(cancel(color(red)(3))))
y = 13/12
Step 3) Substitute 13/12 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = -1 + 3y becomes:
x = -1 + (3 * 13/12)
x = -1 + 39/12
x = (12/12 * -1) + 39/12
x = -12/12 + 39/12
x = 27/12
x = (3 xx 9)/(3 xx 4)
x = (color(red)(cancel(color(black)(3))) xx 9)/(color(red)(cancel(color(black)(3))) xx 4)
x = 9/4
The solution is: x = 9/4 and y = 13/12 or (9/4, 13/12)
