# Use the method of substitution to solve the system of linear equation 4a=2-b 4a=3-b What is the solution?

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### 1 Answer

Substitution means: solve for one of the variables, then substitute that into the other equation.

You can solve for either variable, so here I'm going to do b:

`4a=2-b`

`b=2-4a`

So everywhere you see a b you can replace it with 2-4a

So in the other equation:

`4a=3-b`

Substitute in for b:

`4a=3-(2-4a)`

`4a=1+4a`

`0=1`

This can't happen, so there are no solutions.

PS:

In general, the substitution method is:

take one of the equations

solve for one of the variables

replace that variable in the other equation

solve for the remaining variable

BUT in this case, you can actually make it a little simpler:

`4a=2-b`

So everywhere you see a 4a, you may replace it with 2- b

so in the other equation, `4a=3-b` you may replace the 4a

You get: `2-b=3-b`

So: `2=3`

Again, this can't happen, so there are no solutions