solve by the substitution method: 7x+5y=19 x=29-4y?

7x+5y=19 eq1
x=29-4y eq2

7(29-4y)+5y=19
203-28y+5y=19
203-23y=19
-23y=19-203
-23y=-184
y=8 answer//

plug in y=8 to eq2

x=29-4(8)
x=29-32
x=-3 answer//

x in terms of y—1st equation:
7x + 5y = 19
x = (19 - 5y)/7

Value of y:
7(29 - 4y) = 19 - 5y
203 - 28y = 19 - 5y
23y = 184
y = 8

Value of x (1st equation):
= (19 - 5[8])/7
= (19 - 40)/7
= - 21/7 or - 3

Answer: x = - 3, y = 8

Proof (2nd equation):
- 3 = 29 - 4(8)
- 3 = 29 - 32
- 3 = - 3

7 ( 29 - 4 y ) + 5 y = 19
203 - 28 y + 5 y = 19
184 = 23 y
y = 8

x = 29 - 32
x = - 3

x = - 3 , y = 8

7x + 5y = 19
x = 29 - 4y

7(29 - 4y) + 5y = 19
203 - 28y + 5y = 19
184 = 23y
y = 8
x = 29 - 4* 8 = 29 - 32 = -3

7x+5y=19
x=29-4y

7(29-4y) + 5y = 19
203 - 28y + 5y = 19
203 - 23y = 19
203 - 19 = 23y
184 = 23y
y = 8

put y = 8 into 7x + 5y = 19
7x + 5(8) = 19
7x + 40 = 19
40 - 19 = -7x
21 = -7x
x = -3

7x + 5y = 19 and x = 29 - 4y

since you have an equation for what x equals (29 - 4y), use it in the first equation for x:
7(29 - 4y) + 5y = 19

distribute the 7 through the parenthesis:
203 - 28y + 5y = 19
203 - 23y = 19

subtract 203 from each side:
203 - 23y - 203 = 19 - 203
-23y = -184

divide both sides by -23:
-23y/-23 = -184/-23
**y = 8**

now that you have what y equals (8), plug it into the second equation for y:
x = 29 - 4(8)
x = 29 - 32
**x = -3**

(-3, 8)

hope this helps(:

7x+5y=19
x=29-4y
7(29-4y)+5y=19
203-28y+5y=19
184-23y=0
184=23y
8=y
x=29-4(8)=29-32=-3

203-28y+5y=19 replesing x from 2
23y=184
8=y
x=29-32
x=-3

Check out my Math Variety blog posts on how to solve a system of two linear equations and two unknowns by using the substitution method. I have practice problems and solutions on this topic. http://mathvariety.blogspot.com/2009/04/solving-system-of-two-linear-equations.html
http://mathvariety.blogspot.com/2009/05/solving-system-of-two-linear-equations.html
http://mathvariety.blogspot.com/2009/05/solving-system-of-two-linear-equations_28.html

You already know x=29-4y. Plug this in for x in the first equation and solve for y:
7(29-4y)+5y=19
203-28y+5y=19
203-23y=19
-23y= -184
y=8

Now plug this y value into either equation and solve for x. I'll use the second equation so:
x=29-4y
x=29-4(8)
x=29-32
x= -3

So, x= -3, y=8.

7x + 5y = 19
x = (29 - 4y) ...... (1)

7x + 5y = 19

Substitute (1) for x.
7(29 - 4y) + 5y = 19
203 - 28y + 5y = 19
-28y + 5y = -203 + 19
-23y = -184
y = -184/(-23)
y = 8

x = 29 - 4y

Substitute 8 for y.
x = 29 - 4(8)
x = 29 - 32
x = -3

∴ x = -3, y = 8