algebra
posted by Erica on .
I have to solve this equation using substitution.
3x+5y=10
2x+ 1/2y=24
This is all one problem

2 x + ( 1 / 2 ) y = 24 Multiply both sides by 10
20 x + ( 1 / 2 ) y * 10 = 24 * 10
20 x + 5 y = 240
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3 x + 5 y = 10

20 x + 5 y = 240
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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 
using substitution:
multiply the 2nd by 2
4x + y = 48
y = 484x
sub into the 1st
3x + 5(484x) = 10
3x + 240  20x = 10
17x = 230
x = 230/17
then y = 484(230/7) = 104/17