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Chapter 5: Q. 151 (page 626)

Solve a System of Equations by Elimination -

3x+8y=675x+3y=60

Short Answer

Expert verified

The simplification of Expression will be - (9,5).

Step by step solution

01

Step 1.  Given Information.

Equation - 3x+8y=675x+3y=60

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 -

3x+8y=675x+3y=60

We can eliminate y's by multiplying the first equation by 3 and second equation by 8 -

(3x+8y)脳3=67脳3(5x+3y)脳8=60脳89x+24y=20140x+24y=480

04

Step 4.  Calculation

The equation become -

9x+24y=20140x+24y=480

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

9x+24y=20140x+24y=480-31x=-279

Solve for x -

x=9

Substitute x=9into the second equation5x+3y=60, Then Solve for y -

5x+3y=605脳9+3y=6045+3y=603y=60-453y=15y=5

Written as (x,y)will be (9,5)

05

Step 5.  Check the answer

Check that the ordered pair is a solution to both original equations -

Put (9,5)in the equations -

3x+8y=673脳9+8脳5=6727+40=6767=675x+3y=605脳9+3脳5=6045+15=6060=60

The Solution is - (9,5)

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