# algebra

posted by .

I have to solve this equation using substitution.

3x+5y=10
2x+ 1/2y=24

This is all one problem

• algebra -

2 x + ( 1 / 2 ) y = 24 Multiply both sides by 10

20 x + ( 1 / 2 ) y * 10 = 24 * 10

20 x + 5 y = 240

________________________________________

3 x + 5 y = 10

-

20 x + 5 y = 240
________________________________________

3 x - 20 x + 5 y - 5 y = 10 - 240

- 17 x = - 230 Divide both sides by - 17

- 17 x / - 17 = - 230 / - 17

x = 230 / 17

2 x + 1 / 2 y = 24

2 * 230 / 17 + ( 1 / 2 ) y = 24

460 / 17 + ( 1 / 2 ) y = 24 Subtract 460 / 17 to both sides

460 / 17 + ( 1 / 2 ) y - 460 / 17 = 24 - 460 / 17

( 1 / 2 ) y = 24 - 460 / 17

( 1 / 2 ) y = 24 * 17 / 17 - 460 / 17

( 1 / 2 ) y = 408 / 17 - 460 / 17

( 1 / 2 ) y = - 52 / 17 Multiply both sides by 2

y = - 104 / 17

Solutions :

x = 230 / 17 , y = - 104 / 17

• algebra -

using substitution:
multiply the 2nd by 2
4x + y = 48
y = 48-4x

sub into the 1st
3x + 5(48-4x) = 10
3x + 240 - 20x = 10
-17x = -230
x = 230/17
then y = 48-4(230/7) = -104/17