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Chapter 5: Q. 140 (page 626)

Solve a System of Equations by Elimination -

-x+4y=83x+5y=10

Short Answer

Expert verified

The simplification of Expression will be (0,2).

Step by step solution

01

Step 1.  Given Information.

Equation - -x+4y=83x+5y=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 -

-x+4y=83x+5y=10

We can eliminate y's by multiplying the first equation by 5 and second equation by 4 -

(-x+4y)脳5=8脳5(3x+5y)脳4=10脳4-5x+20y=4012x+20y=40

04

Step 4.  Calculation

The equation become -

-5x+20y=4012x+20y=40

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

-5x+20y=4012x+20y=40-17x=0

Solve for x -

x=0

Substitute x=0into the second equation 3x+5y=10, Then Solve for y -

3x+5y=103脳0+5y=100+5y=105y=10y=2

Written as (x,y)will be (0,2)

05

Step 5.  Check the answer

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

Put (0,2)in the equations -

-x+4y=8-(0)+4脳2=80+8=88=8

3x+5y=103脳0+5脳2=100+10=1010=10

The Solution is (0,2)

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