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Mathematics
Deegan Obrien
4 April, 13:18
If 5a+4b=25 and 3a-8b=41, solve for a And b
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Brogan Bradshaw
4 April, 13:44
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a = 7
b = - 5 / 2
Let's solve your system by substitution.
5a+4b=25 and 3a-8b=41
Rewrite equations:
5a+4b=25; 3a-8b=41
Step: Solve5a+4b=25for a:
5a+4b=25
5a+4b+-4b=25+-4b (Add - 4b to both sides)
5a=-4b+25
5a = - 4b+25
5 a/5 = - 4b+25 / 5
(Divide both sides by 5)
a = - 4 / 5 b + 5
Step: Substitute
-4 / 5 b+5 for a in 3a-8b=41:
3a-8b=41
3 (-4 / 5 b+5) - 8b=41
-52 / 5 b+15=41 (Simplify both sides of the equation)
-52 / 5 b+15+-15=41+-15 (Add - 15 to both sides)
-52 / 5 b=26
-52 / 5 b / -52 / 5 = 26 / -52 / 5
(Divide both sides by (-52) / 5)
b = - 5 / 2
Step: Substitute - 5 / 2 for b in a = - 4 / 5 b+5:
a = - 4 / 5 b+5
a = - 4 / 5 (-5 / 2) + 5
a=7 (Simplify both sides of the equation)
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