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Chapter 5: Q. 5.37 (page 605)

Solve the system by substitution.

2x鈭�3y=12鈭�12y+8x=48

Short Answer

Expert verified

The system has infinitely many solutions.

Step by step solution

01

Step 1. Given Information  

We have to solve the system by substitution.

2x鈭�3y=12鈭�12y+8x=48

02

Step 2. Firstly solving the equation 2x−3y=12 for the variable x.

Add3yonbothside2x鈭�3y+3y=12+3y2x=12+3yDivideby2onbothside22x=12(12+3y)x=12(12+3y)

03

Step 3. Putting the value of x in the equation −12y+8x=48. 

鈭�12y+8路12(12+3y)=48鈭�12y+4(12+3y)=48鈭�12y+48+12y=4848=48

04

Step 4. Since 48=48 is a true statement, the system is consistent.

The equations are dependent. The graphs of these two equations would give the same line. The system has infinitely many solutions.

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