Use Substitution to solve 12c + 8t = 34 and 10c + 7t = 29
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Use the substitution method to solve:
12c + 8t = 34
10c + 7t = 29
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:
10c + 7t = 29
Subtract 7t from both sides to isolate c:
10c + 7t - 7t = 29 - 7t
10c = 29 - 7t
Now divide by 10:
10c
10
=
29 - 7t
10
Revised Equation 2:
c =
29 - 7t
10
Plug Revised Equation 2 value into c:
12(c) + 8t = 34
12 * ((29 - 7t)/10) + 8t = 34
((348 - 84t)/10) + 8t = 34
Multiply equation 1 through by 10
10 * (((348 - 84t)/10) + 8t = 34)
10 * (((348 - 84t)/10) + 8t = 34)
348 - 84t + 80t = 340
Group like terms:
-84t + 80t = 340 - 348
-4t = -8
Divide each side by -4
-4t
-4
=
-8
-4
t =
-8
-4
t = 2
Plug this answer into Equation 1
12c + 8(2) = 34
12c + 16 = 34
12c = 34 - 16
12c = 18
Divide each side by 12
12c
12
=
18
12
c =
18
12
c = 1.5
What is the Answer?
c = 1.5 and t = 2
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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