Question

can someone solve for x+y=10 and 10x+15y=115

Answer 1

x + y = 10
10x + 15y = 115


Lets solve the top equation for 'y'

x + y = 10
-x -x
-----------
y = -x + 10

Now that we know what y equals...lets plug it into the second equation for every 'y' we see..

10x + 15y = 115 becomes

10x + 15(-x + 10) = 115

Distribute that 15 into the parenthesis...

10x - 15x + 150 = 115

Combine like terms...

-5x + 150 = 115

Subtract 150 from both sides...

-5x = -35

Divide both sides by -5

x = 7

Answer 2

Now that we know x = 7...we can solve for 'y'

x + y = 10 right? well if 'x' = 7...y = ?

7 + y = 10
y = 3

So we have x = 7 and y = 3....is that correct...lets check with out 2nd given equation...

10x + 15y = 115
10(7) + 15(3) = 115
70 + 45 = 115
115 = 115 \(\large \color \red {\checkmark} \)