SOLUTION: if (2a + b = 80) and (2b + a = 76) then a = ?

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Question 181775: if (2a + b = 80) and (2b + a = 76) then a = ?
Found 2 solutions by Earlsdon, solver91311:
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
If (2a+b= 80) and (2b+a = 76) then a =?
2a+b = 80 Rewrite this as b = 80-2a and substitute into the 2nd equation.
2b+a = 76
2(80-2a)+a = 76 Simplify.
160-4a+a = 76
160-3a = 76 Subtract 160 from both sides.
-3a = -84 Divide both sides by -3.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

You can do this either by substitution or elimination.

Substitution

Step 1: Solve the first equation for b

Step 2: Substitute the expression in a for b in the 2nd equation:

Step 3: Solve this new equation for a:

From here you could substitute 28 for a in either of the original equations and then solve for b if you needed to.

Elimination

Step 1: Rearrange the equations so that the variables are in the same order:

Step 2: Multiply the 1st equation by -2:

Step 3: Add this new form of 1st equation to the 2nd equation term by term and solve for a:

Same result.
John