SOLUTION: Solve and then check the system of equations by substitution method. SHOW ALL WORK STEP BY STEP! 4a+7b=2 5a+b=-13

Algebra ->  Linear-equations -> SOLUTION: Solve and then check the system of equations by substitution method. SHOW ALL WORK STEP BY STEP! 4a+7b=2 5a+b=-13      Log On


   

Question 969444: Solve and then check the system of equations by substitution method. SHOW ALL WORK STEP BY STEP!
4a+7b=2
5a+b=-13
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
4a=-7b%2B2
a=-%287%2F4%29b%2B2

substitution:
5%282-%287%2F4%29b%29%2Bb=-13

10-35b%2F4%2Bb=-13
-35b%2F4%2Bb=-23
35b%2F4-b=23
35b-4b=92
31b=92
highlight%28b=92%2F31%29

Now find value for a.
a=2-%287%2F4%29b
a=2-%287%2F4%29%2892%2F31%29
a=2-%287%2A92%29%2F%284%2A31%29
a=%282%284%2A31%29-7%2A92%29%2F%284%2A31%29
a=-396%2F%284%2A31%29
highlight%28a=-99%2F31%29

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Solve and then check the system of equations by substitution method. SHOW ALL WORK STEP BY STEP!
4a+7b=2
5a+b=-13
4a + 7b =    2 -------- eq (i)

5a +  b = - 13______b+=+%28-+13+-+5a%29 -------- eq (ii)

4a + 7(- 13 - 5a) = 2 ------ Substituting - 13 - 5a for b in eq (i)

4a - 91 - 35a = 2

4a - 35a = 2 + 91

- 31a = 93

highlight_green%28a+=+-+93%2F31%29

Substitute -+93%2F31 for a in eq (i) or eq (ii) to determine value of b