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Chapter 11: Q. 38 (page 729)

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

x+2y=5x+y=3

Short Answer

Expert verified

The required solution isx=1,y=2

Step by step solution

01

Step 1. Given Information 

The given equations are

x+2y=5x+y=3

02

Step 2. Calculation 

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

12|511|3

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

12|511|3=12|51-11-2|3-5=12|50-1|-2

03

Step 3. Calculation 

Use the obtained matrix to write the system of equations.

x+2y=5-y=-2

Solve the equations to find the solution set.

y=2x+2(2)=5x+4=5x=1

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Most popular questions from this chapter

The sum of two numbers is the same as their product, and the difference of their reciprocals is 3. Find the numbers.

In Problems 23鈥�34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

x-2y鈮�62x-4y鈮�0

Solve each system of equations. If the system has no solution, say that it is inconsistent.

3x-2y+2z=67x-3y+2z=-12x-3y+4z=0

Graph the equation:y+4=x2

In Problems 23鈥�34, graph each system of linear inequalities by hand. Verify your results using a graphing utility

2x+y鈮�02x+y鈮�2
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