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

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)