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# Use the method of substitution to solve the system of linear equations.

7a=6-b

7a=4-b

Select the correct choice below and if letter a is chosen type an ordered pair.

(a) There is one solution.

(b) There is infinitely many solutions.

(c) There are no solutions.

### 1 Answer by Expert Tutors

Kristy W. | Mathematics Tutor with Masters in Math and a Certified TeacherMathematics Tutor with Masters in Math a...
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First you pick one of the equations and solve for one of the variables.  You can pick either equation. Let's pick the first equation and solve for b:

First we subtract 6 from both sides:  7a-6=-b

Next we multiply both sides by -1 in order to get the value of b:  -7a+6=b

Now that we have solved for b in the first equation, we plug the value of b into the second equation:

7a=4-(-7a+6)

On the right hand side of the equation, we distribute the negative into the parenthesis: 7a=4+7a-6

Then to get the a's on the same side, we subtract 7a from both sides:  0=4-6

Simplifying the right hand side we get 0=-2.  Since this is a false statement, then our method of substitution has shown us that the answer is (c) There are no solutions.