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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mlehuzzah | Student, Graduate | (Level 1) Associate Educator

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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 

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