Use the elimination method to solve the system of equations.

Question

a+6b=13

a+4b=7

Select the correct choice

(a) There is one solution, it is what (Simplify your answer type a ordered pair must be a ordered pair)

(b) There are infinitely many solutions

(c) There is no solution

Answer 1

The correct answer is (a). The solution is a=-5 and b=3. This is  (-5,3) written as an ordered pair.

a+6b=13

a+4b=7

We want to get rid of one variable (a or b) and so we need to either add or subtract one equation from the other. 

1) Subtract equation 2 (the bottom one) from equation 1. 

   a+6b=13

 - a+4b=7

        2b=6 

The variable a is eliminated as a minus a leaves nothing. As seen above only one variable (b) remains.

2) Solve new equation to find b.

         2b=6

           b=6/2

           b=3

3) Replace b with 3 in either equations to find the value of a.

          a+6b=13

          a+6(3)=13

          a+18=13

                a=13-18

                 a=-5

Therefore there is one solution : a=-5 and b=3. This can be written as (-5,3).

You can plug these values into the other equation to check if they are correct.