Finite Math Examples

4x-5y=-5 , 3x-y=1
Step 1
Write the system as a matrix.
[4-5-53-11]
Step 2
Find the reduced row echelon form.
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Step 2.1
Multiply each element of R1 by 14 to make the entry at 1,1 a 1.
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Step 2.1.1
Multiply each element of R1 by 14 to make the entry at 1,1 a 1.
[44-54-543-11]
Step 2.1.2
Simplify R1.
[1-54-543-11]
[1-54-543-11]
Step 2.2
Perform the row operation R2=R2-3R1 to make the entry at 2,1 a 0.
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Step 2.2.1
Perform the row operation R2=R2-3R1 to make the entry at 2,1 a 0.
[1-54-543-31-1-3(-54)1-3(-54)]
Step 2.2.2
Simplify R2.
[1-54-540114194]
[1-54-540114194]
Step 2.3
Multiply each element of R2 by 411 to make the entry at 2,2 a 1.
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Step 2.3.1
Multiply each element of R2 by 411 to make the entry at 2,2 a 1.
[1-54-544110411114411194]
Step 2.3.2
Simplify R2.
[1-54-54011911]
[1-54-54011911]
Step 2.4
Perform the row operation R1=R1+54R2 to make the entry at 1,2 a 0.
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Step 2.4.1
Perform the row operation R1=R1+54R2 to make the entry at 1,2 a 0.
[1+540-54+541-54+541911011911]
Step 2.4.2
Simplify R1.
[101011011911]
[101011011911]
[101011011911]
Step 3
Use the result matrix to declare the final solution to the system of equations.
x=1011
y=1911
Step 4
The solution is the set of ordered pairs that make the system true.
(1011,1911)
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