Use Substitution to solve 2a + 3k = 51 and 3a + k = 45
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Use the substitution method to solve:
2a + 3k = 51
3a + k = 45
Check Format
Equation 1 is in the correct format.
Check Format
Equation 2 is in the correct format.
Rearrange Equation 2 to solve for a:
3a + k = 45
Subtract k from both sides to isolate a:
3a + k - k = 45 - k
3a = 45 - k
Plug Revised Equation 2 value into a:
2(a) + 3k = 51
2 * (45 - k) + 3k = 51
((90 - 2k)/3) + 3k = 51
Multiply equation 1 through by 3
3 * (((90 - 2k)/3) + 3k = 51)
3 * (((90 - 2k)/3) + 3k = 51)
90 - 2k + 9k = 153
Group like terms:
-2k + 9k = 153 - 90
7k = 63
Divide each side by 7
7k
7
=
63
7
k =
63
7
k = 9
Plug this answer into Equation 1
2a + 3(9) = 51
2a + 27 = 51
2a = 51 - 27
2a = 24
Divide each side by 2
2a
2
=
24
2
a =
24
2
a = 12
What is the Answer?
a = 12 and k = 9
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
Pick any 3 of the methods to solve the systems of equations
2 equations 2 unknowns This calculator has 2 inputs.
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