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:
 + a = 76)
Step 3: Solve this new equation for a:
 + a = 76\ \ \Rightarrow\ \ 160 - 4a + a = 76\ \ \Rightarrow\ \ 160 - 3a = 76 \cr \text{ }\math \ \ \Rightarrow\ \ -3a = 76 - 160\ \ \Rightarrow\ \ -3a = -84\ \ \Rightarrow\ \ a = 28)
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:
 + (a + 2b) = (-160)+(76) \ \ \Rightarrow\ \ (- 4a + a) + (-2b + 2b) = -84\cr \text{ }\math\ \ \Rightarrow\ \ -3a = -84 \ \ \Rightarrow\ \ a = 28)
Same result.
John
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