Use Substitution to solve 10c + 3s = 82 and 5c + 8s = 67
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Use the substitution method to solve:
10c + 3s = 82
5c + 8s = 67
Check Format
Equation 1 is in the correct format.
Check Format
Equation 2 is in the correct format.
Rearrange Equation 2 to solve for c:
5c + 8s = 67
Subtract 8s from both sides to isolate c:
5c + 8s - 8s = 67 - 8s
5c = 67 - 8s
Now divide by 5:
5c
5
=
67 - 8s
5
Revised Equation 2:
c =
67 - 8s
5
Plug Revised Equation 2 value into c:
10(c) + 3s = 82
10 * ((67 - 8s)/5) + 3s = 82
((670 - 80s)/5) + 3s = 82
Multiply equation 1 through by 5
5 * (((670 - 80s)/5) + 3s = 82)
5 * (((670 - 80s)/5) + 3s = 82)
670 - 80s + 15s = 410
Group like terms:
-80s + 15s = 410 - 670
-65s = -260
Divide each side by -65
-65s
-65
=
-260
-65
s =
-260
-65
s = 4
Plug this answer into Equation 1
10c + 3(4) = 82
10c + 12 = 82
10c = 82 - 12
10c = 70
Divide each side by 10
10c
10
=
70
10
c =
70
10
c = 7
What is the Answer?
c = 7 and s = 4
How does the Simultaneous Equations Calculator work?
Free Simultaneous Equations Calculator - Solves a system of simultaneous equations with 2 unknowns using the following 3 methods: 1) Substitution Method (Direct Substitution) 2) Elimination Method 3) Cramers Method or Cramers Rule
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