Question

Solve this system using the substitution method.
3x + 2y = 10
2x + 3y = 15/2
Answer

No solution

y = (-3/2)x + 5

x = 3, y = -1/2

x = 3, y = 1/2

Answer 1

get y from 1st equation and substitute in 2nd eq

3x + 2y = 10 subtract 3x both sides
2y= 10-3x now divide both sides by 2
2y/2=(10-3x)/2
y=10/2 -3x/2 or
y= 5 -3/2x

now we know y so sub it to 2nd eq

2x + 3(5 -3/2x) = 15/2 mult thru by 3 to get rid of parentheses
2x + 15 -9/2x=15/2 lets get a common denominator of 2

4/2x + 30/2 -9/2x = 15/2 subtract 30/2 both sides
4/2x-9/2x=-15/2 now combine x terms
-5/2x = -15/2 mult both sides by -2/5
x=30/10 or = 3

x = 3 now plug it in both equations and solve for y



also for this step

2x + 15 -9/2x=15/2 i could just mult by 2 and that would get rid of the denominator
4x+30-9x = 15 solve you get the same