This is a substitution equation. Would that change the steps that you did?

Question

Y=3x+1
Y=5x-3
Answer says x=-2 and y=7

Please explain steps. Thanks

math help - MathMate, Monday, April 23, 2012 at 10:25pm
Y=3x+1 ...(1)
Y=5x-3 ...(2)

By comparison of (1) and (2), we conclude that
3x+1=Y=5x-3
3x+1=5x-3
solve for x to get
2x=4
x=2
Put x=2 in (1) to get
Y=3(2)+1=7
Check:
put x=2 in (2) to get
Y=5*2-3=7

If your program gives x=-2 and y=7, there must be a typo somewhere. Check your post

Answer 1

y = 3 x + 1

y - 1 = 3 x Divide both sides by 3

( y - 1 ) / 3 = x

x = ( y - 1 ) / 3

y = 5 x - 3

y = 5 * ( y - 1 ) / 3 - 3

y = ( 5 / 3 ) * ( y - 1 ) - 3

y = 5 y / 3 - 5 / 3 - 3

y = 5 y / 3 - 5 / 3 - 9 / 3

y = 5 y / 3 - 14 / 3

y - 5 y / 3 = - 14 / 3

3 y / 3 - 5 y / 3 = - 14 / 3

- 2 / 3 y = - 14 / 3 Multiply both sides by - 3

2 y = 14 Divide both sides by 2

y = 14 / 2

y = 7

x = ( y - 1 ) / 3

x = ( 7 - 1 ) / 3

x = 6 / 3

x = 2

x = 2 , y = 7

Or very simply :

y = 3 x + 1

y = 5 x - 3

3 x + 1 = 5 x - 3

3 x - 5 x = - 3 - 1

- 2 x = - 4 Divide both sides by - 2

- 2 x / - 2 = - 4 / - 2

x = 2

y = 3 x + 1

y = 3 * 2 + 1 = 6 + 1 = 7

y = 5 x - 3

y = 5 * 2 - 3 = 10 - 3 = 7

x = 2 , y = 7