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Chapter 4: Q. 4.17 (page 380)

Solve the system by elimination:3x+y=52x-3y=7

Short Answer

Expert verified

The solution of the system of equations is (2,-1).

Step by step solution

01

Step 1. Given Information.

We have been given system of equations3x+y=52x-3y=7

02

Step 2. Eliminate the y's by multiplying a number in first equation.

Multiply both sides of 3x+y=5by 3,

3(3x+y)=3(5)2x-3y=7

localid="1644378022840" 9x+3y=152x-3y=7

03

Step 3. Add the equations resulting from Step 2 to eliminate one variable and solve it.

Add the x's,y'sand constants.

9x+3y=152x-3y=7

11x=22

x=2

04

Step 4. Substitute the solution from Step 3 into one of the original equation and solve for the other variable.

Substitute x=2into the first equation.

3x+y=5

3(2)+y=5

6+y=5

y=-1

05

Step 5. Write the solution as an ordered pair.

Write it as (x,y).

(2,-1)
06

Step 6. Check that the ordered pair is a solution to both original equations. 

Substitute x,y=2,-1into both original equations.

3x+y=5

3(2)-1=5

5=5

And,

2x-3y=7

2(2)-3(-1)=7

4+3=7

7=7

Both equations are True.

The point (2,-1)is the solution to the system.

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