Question

If 5a+4b=25 and 3a-8b=41, solve for a And b

Answer 1

Answer:

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)