Use Substitution to solve 4d + 3p = 33.50 and 6d + 5p = 54
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Use the substitution method to solve:
4d + 3p = 33.50
6d + 5p = 54
Check Format
Equation 1 is in the correct format.
Check Format
Equation 2 is in the correct format.
Rearrange Equation 2 to solve for d:
6d + 5p = 54
Subtract 5p from both sides to isolate d:
6d + 5p - 5p = 54 - 5p
6d = 54 - 5p
Now divide by 6:
6d
6
=
54 - 5p
6
Revised Equation 2:
d =
54 - 5p
6
Plug Revised Equation 2 value into d:
4(d) + 3p = 33.50
4 * ((54 - 5p)/6) + 3p = 33.50
((216 - 20p)/6) + 3p = 33.50
Multiply equation 1 through by 6
6 * (((216 - 20p)/6) + 3p = 33.50)
6 * (((216 - 20p)/6) + 3p = 33.50)
216 - 20p + 18p = 201
Group like terms:
-20p + 18p = 201 - 216
-2p = -15
Divide each side by -2
-2p
-2
=
-15
-2
p =
-15
-2
p = 7.5
Plug this answer into Equation 1
4d + 3(7.5) = 33.50
4d + 22.5 = 33.50
4d = 33.50 - 22.5
4d = 11
Divide each side by 4
4d
4
=
11
4
d =
11
4
d = 2.75
What is the Answer?
d = 2.75 and p = 7.5
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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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