Algebra Examples
4x−y=−4 , 3x−3y=−6
Step 1
Write the system of equations in matrix form.
[4−1−43−3−6]
Step 2
Step 2.1
Multiply each element of R1 by 14 to make the entry at 1,1 a 1.
Step 2.1.1
Multiply each element of R1 by 14 to make the entry at 1,1 a 1.
[44−14−443−3−6]
Step 2.1.2
Simplify R1.
[1−14−13−3−6]
[1−14−13−3−6]
Step 2.2
Perform the row operation R2=R2−3R1 to make the entry at 2,1 a 0.
Step 2.2.1
Perform the row operation R2=R2−3R1 to make the entry at 2,1 a 0.
[1−14−13−3⋅1−3−3(−14)−6−3⋅−1]
Step 2.2.2
Simplify R2.
[1−14−10−94−3]
[1−14−10−94−3]
Step 2.3
Multiply each element of R2 by −49 to make the entry at 2,2 a 1.
Step 2.3.1
Multiply each element of R2 by −49 to make the entry at 2,2 a 1.
⎡⎢⎣1−14−1−49⋅0−49(−94)−49⋅−3⎤⎥⎦
Step 2.3.2
Simplify R2.
[1−14−10143]
[1−14−10143]
Step 2.4
Perform the row operation R1=R1+14R2 to make the entry at 1,2 a 0.
Step 2.4.1
Perform the row operation R1=R1+14R2 to make the entry at 1,2 a 0.
[1+14⋅0−14+14⋅1−1+14⋅430143]
Step 2.4.2
Simplify R1.
[10−230143]
[10−230143]
[10−230143]
Step 3
Use the result matrix to declare the final solutions to the system of equations.
x=−23
y=43
Step 4
The solution is the set of ordered pairs that makes the system true.
(−23,43)
Step 5
Decompose a solution vector by re-arranging each equation represented in the row-reduced form of the augmented matrix by solving for the dependent variable in each row yields the vector equality.
X=[xy]=[−2343]
