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Chapter 11: Q. 44 (page 729)

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

12x+y=-2x-2y=8

Short Answer

Expert verified

The required solution isx=2,y=-3

Step by step solution

01

Step 1. Given Information 

The given equations are

12x+y=-2x-2y=8

02

Step 2. Calculation 

We will first write the augmented matrix, by writing constants on right side of vertical bar.

121|-21-2|8

Now, we will make the entry 0 in row 2 column 1 by performing the row operations R1=2R1and then apply the operation R2=-R1+R2

121|-21-2|8=2(12)2(1)|2(-2)1-2|8=12|-41-2|8=12|-4-1+1-2-2|-(-4)+8=12|-40-4|12

03

Step 3. Calculation 

Use the obtained matrix to write the system of equations.

x+2y=-4-4y=12

Solve the equations to find the solution set.

-4y=12鈬�y=-3x+2(-3)=-4x-6=-4x=-4+6x=2

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