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Chapter 11: Q. 53 (page 794)

Find A so that the system of equations has infinitely many
solutions.

2x+5y=54x+10y=A

Short Answer

Expert verified

The system of equation has infinitely many solutions when A=10

Step by step solution

01

Step 1. Given

The system of equations:

2x+5y=54x+10y=A

02

Step 2. Solve the first equation for y

Solve the first equation for y.

2x+5y=55y=5-2xy=5-2x5

03

Step 3. Substitute y in second equations.

Substitute y=5-2x5in the second equation,

4x+10(5-2x5)=A4x+10-4x=AA=10

The system has infinitely many solution when A=10

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Most popular questions from this chapter

In Problems 5鈥�24, graph each equation of the system. Then solve the system to find the points of intersection.

x2+y2=4;y2-x=4

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

Graph each equation of the system. Then solve the system to find the points of intersection.

y=x2+1y=x+1

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

x+2y=42x+4y=8

Verify that the values of the variables listed are solutions of the system of equations.

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