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Chapter 5: Q. 160 (page 626)

Solve a System of Equations by Elimination -
4x+3y=220x+15y=10

Short Answer

Expert verified

This is a true statement. The equations are consistent but dependent. Their graphs would be the same line. The system has infinitely many solutions.

Step by step solution

01

Step 1.  Given Information.

Equation - 4x+3y=220x+15y=10

02

Step 2.  To Find

Solve a System of Equations by Elimination and find the value of x and y.

03

Step 3.  Explanation

Equation -

4x+3y=220x+15y=10

We can eliminate y's by multiplying the first equation by 5 -

(4x+3y)脳5=2脳520x+15y=1020x+15y=1020x+15y=10

04

Step 4.  Calculation

The equation become -

20x+15y=1020x+15y=10

We subtract the x's and y's and constants -

20x+15y=1020x+15y=100=0

This is a true statement. The equations are consistent but dependent. Their graphs would be the same line. The system has infinitely many solutions.

After we cleared the fractions in the second equation, did you notice that the two equations were the same? That means we have coincident lines.

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