7x-3y=3 x= 2y+ 2 solve system of linear equation by the substitution method?

Question

Solve system of linear equation by the substitution method:

7x-3y=3
x= 2y+2

Answer 1

Just take the second equation and replace it for x in the first equation:
7(2y+2)-3y=3
14y+14-3y=3
11y+14=3
11y=-11
y=-1

x=2(-1)+2
x=-2+2
x=0

The solution set is (0,-1)

Check:
7(0)-3(-1)=3
3=3

0=-2+2
0=0

I hope this helps!

Answer 2

By substituting x we get,

7 (2y+2) -3y =3

14y+14-3y=3

11y=3-14

11y =-11

y= -1

x =2y +2(given)

x =2(-1)+2

x =-2+2=0

Therefore, x=0
y= -1

Answer 3

this is how my math teacher taught it:
7x-3y=3
x=2y+2

plug in 2y+2 everywhere you see an x.

7(2y+2)-3y=3

use the distributive property

7 times 2y=14y
7 times 2=14

14y+14-3y=3

14y-3y=11y
11y-14=3
add 14 to both sides

11y=-11
divide both sides by 11
y=-1

plug in negative 1 to ONE of the first equations. i choose x=2y+2

x=2(-1)+2

2 times -1=-2
-2+2 cancel each other out
x=0

write the answer like this {0,-1}

Answer 4

7x-3y=3
x= 2y+2

Substitute the second equation in the first, ie

7(2y + 2) -3y = 3 ==> 14y +14 -3y = 3 ==> 11y = -11 ==> y = -1

Substitute thus value of y in the second to obtain x = 2x(-1) + 2 = 0

Answer 5

7x - 3y = 3
x = 2y + 2

Plug the value of x from the second equation into the first.

7x - 3y = 3
7(2y + 2) - 3y = 3
14y + 14 - 3y = 3
11y = -11
y = -1

x = 2y + 2 = 2(-1) + 2 = -2 + 2 = 0

x = 0
y = -1

Answer 6

14y+14-3y=3
11y=-11
y=-1
x=-2+2=0
Therefore, x=0, y=-1

Answer 7

x=2y+2
7(2y+2)-3y=3
14y+14-3y=3
11y+14=3
11y=-11
y=-1
x=2(-1)=2
x=-2+2
x=0

(0,-1)