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Chapter 4: Q 56 (page 386)

In the following exercise, solve the systems of equations by elimination.

13x-y=-3x+52y=2

Short Answer

Expert verified

The solution is(-3,2).

Step by step solution

01

Step 1. Given information

The given equations are

13x-y=-3

x+52y=2

02

Step 2. Calculating the value of y

To calculate the value of ywe have to eliminate the x'sterm.

Let us do some changes through which we can easily eliminate x.

1) multiply the first equation by-3

-313x-y=-3

-x+3y=9

now, the new equations are

-x+3y=9x+52y=2

just add the equations

-x+3y=9x+52y=2112y=11

y=2

the value ofy=2

03

Step 3. Calculating the value of x

As we have the value of y, we can substitute it in any equation and hence calculate the value of x.

let us take the first equation

13x-y=-3

put y=2

13x-2=-313x=-1x=-3

the value of x is -3.

04

Step 4. Checking the solution 

Checking the solution by putting the value of x,yin the equation, we get

13x-y=-313(-3)-2=-3-1-2=-3-3=-3x+52y=2-3+52(2)=2-3+5=22=2

This is true, hence the solution is correct.

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