Step 1) Solve the first equation for aa:
a + 3b = 7a+3b=7
a + 3b - color(red)(3b) = 7 - color(red)(3b)a+3b−3b=7−3b
a + 0 = 7 - 3ba+0=7−3b
a = 7 - 3ba=7−3b
Step 2) Substitute (7 - 3b)(7−3b) for aa in the second equation and solve for bb:
2a = b - 72a=b−7 becomes:
2(7 - 3b) = b - 72(7−3b)=b−7
(2 * 7) - (2 * 3b) = b - 7(2⋅7)−(2⋅3b)=b−7
14 - 6b = b - 714−6b=b−7
14 + color(blue)(7) - 6b + color(red)(6b) = b + color(red)(6b) - 7 + color(blue)(7)14+7−6b+6b=b+6b−7+7
21 - 0 = 1b + color(red)(6b) - 021−0=1b+6b−0
21 = (1 + color(red)(6))b21=(1+6)b
21 = 7b21=7b
21/color(red)(7) = (7b)/color(red)(7)217=7b7
3 = (color(red)(cancel(color(black)(7)))b)/cancel(color(red)(7))
3 = b
b = 3
Step 3) Substitute 3 for b in the solution to the first equation at the end of Step 1 and calculate a:
a = 7 - 3b becomes:
a = 7 - (3 * 3)
a = 7 - 9
a = -2
The Solution Is:
a = -2 and b = 3
