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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.

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.