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Chapter 11: Q. 1 (page 793)

In Problems 1鈥�10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

2x-y=55x+2y=8

Short Answer

Expert verified

The solution of the system is2,-1.

Step by step solution

01

Step 1. Given Information

We are given a system of equation 2x-y=55x+2y=8.

We need to solve the system using the method of substitution or the method of elimination.

02

Step 2. Eliminate the variable y and solve for x

Multiply both sides of the first equation 2x-y=5by 2

role="math" 2(2x-y)=2路54x-2y=10

Now add this equation with the first equation and solve for x.

5x+2y+(4x-2y)=8+105x+2y+4x-2y=189x=18x=189x=2

03

Step 3. Solve for y

Substitute 2for xin the first equation and solve for y.

2x-y=52路2-y=54-y=5-y=5-4-y=1y=-1

So the solution of the system is the ordered pair 2,-1.

04

Step 4. Check the solution

Substitute 2for xand -1for yin both the equations.

2x-y=52路2-(-1)=54+1=55=55x+2y=85路2+2(-1)=810-2=88=8

So both the equations are satisfied. Thus the found solution is correct.

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