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Chapter 5: Q. 102 (page 611)

In the following exercises, solve the systems of equations by substitution.

15x+4y=6-30x-8y=-12

Short Answer

Expert verified

The equations have infinitely many solutions.

Step by step solution

01

Step 1. Given Information  

The given equations are

15x+4y=6-30x-8y=-12

02

Step 2. Calculation   

Solve the second equation for variable y.

-30x-8y=-12-8y=-12+30xy=-12+30x-8y=32-154x

Substitute the obtained value of variable y in the first equation to find the value of variable x.

15x+4y=615x+4(32-154x)=615x+6-15x=66=6

Since 6=6is a true statement, the system is consistent. The equations are dependent. The graph of these two equations would give the same line. Thus the system of the linear equation has infinitely many solutions.

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