Answer:
m = 3, n = 4
Step-by-step explanation:
Solve using the substitution process. First, start with the second equation:
2m + 2n = 14
Simplify. Divide 2 from all terms within the equation. What you do to one side, you do to the other:
(2m + 2n)/2 = (14)/2
m + n = 7
Isolate the variable m. Subtract n from both sides:
m + n (-n) = 7 (-n)
m = 7 - n
Plug in 7 - n for m in the first equation:
-5m + 9n = 21
-5(7 - n) + 9n = 21
Solve. First, distribute -5 to all terms within the parenthesis:
(-35 + 5n) + 9n = 21
Simplify. Combine like terms:
-35 + (5n + 9n) = 21
-35 + 14n = 21
Isolate the variable, n. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, add 35 to both sides:
14n - 35 (+35) = 21 (+35)
14n = 21 + 35
14n = 56
Isolate the variable n. Divide 14 from both sides:
(14n)/14 = (56)/14
n = 56/14
n = 4
Plug in 4 to n in one of the equations, and solve for m.
2m + 2n = 14
2m + 2(4) = 14
2m + 8 = 14
Isolate the variable, m. Do the opposite of PEMDAS. First, subtract 8 from both sides:
2m + 8 (-8) = 14 (-8)
2m = 14 - 8
2m = 6
Divide 2 from both sides:
(2m)/2 = (6)/2
m = 6/2
m = 3
Your answers: m = 3, n = 4
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