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Chapter 5: Q. 145 (page 626)

Solve a System of Equations by Elimination -

3x-5y=-95x+2y=16

Short Answer

Expert verified

The simplification of Expression will be - (2,3).

Step by step solution

01

Step 1.  Given Information.

Equation - 3x-5y=-95x+2y=16

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-5y=-95x+2y=16

We can eliminate y's by multiplying the first equation by 2 and second equation by 5 -

(3x-5y)脳2=-9脳2(5x+2y)脳5=16脳56x-10y=-1825x+10y=80

04

Step 4.  Calculation

The equation become -

6x-10y=-1825x+10y=80

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

6x-10y=-1825x+10y=8031x=62

Solve for x -

x=2

Substitute x=2into the second equation 5x+2y=16, Then Solve for y -

5x+2y=165脳2+2y=1610+2y=162y=16-102y=6y=3

Written as (x,y)will be (2,3)

05

Step 5.  Check the answer

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

Put (2,3)in the equations -

3x-5y=-93脳2-5脳3=-96-15=-9-9=-9

5x+2y=165脳2+2脳3=1610+6=1616=16

The Solution is - (2,3)

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