solving systems using substitution?

Question

Please Help

1) y = 2x + 11
y = -x + 5

2)) y = 4x - 3
y = 5x - 1

Answer 1

1) 2x + 11 = -x + 5 (Since both equations equal y, they both equal each other)
3x = -6 (adding x to each side and subtracting 11 from each side)
x = -2 (dividing each side by 3)
y = 2(x) + 11 (substituting x back in to original equation to solve for y)
y = 2(-2) + 11
y = 7

2) 4x - 3 = 5x - 1
x = -2 (subtracting 4x from each side and adding 1 to each side)
y = 4(x) - 3 (substituting x back in to solve for y)
y = 4(-2) - 3
y = -8 - 3
y = -11

Answer 2

1) y = 2x + 11
y = -x + 5

-x+5=2x+11
x=-6
y=-x+5=-6+5=-1

2)) y = 4x - 3
y = 5x - 1

4x-3=5x-1
x=-2
y=4x-3=4*(-2)-3=-8-3=-11

Answer 3

1)

If y=2x+11 and also y=-x+5, then 2x-11=-x+5
From there, just simplify and solve
2x-11=-x+5 (Add X to both sides)
3x-11=5 (The -x is canceled out by adding an x) (add 11 to both sides)
3x=5+11
3x=16
x=16/3, or 5.333333....

2)y=4x-3, y=5x-1
4x-3=5x-1
-3=x-1
-2=x
x=-2

Answer 4

(1) y = 2x + 11 & y = -x + 5

First: substitute (-x + 5) with "y" in the 1st equation.

-x+5 = 2x+11

Sec: combine "like" terms - subtract 2x from both sides (when you move a term to the opposite side, always use the opposite sign).

-x-2x+5 = 2x-2x+11
-3x + 5 = 11 (subtract 5 from both sides).
-3x + 5-5 = 11-5
-3x = 6 (divide both sides by -3).
-3x/-3 = 6/-3
x = -2

third: substitute (-2) with "x" in the 2nd equation.

y = - (-2) + 5
y = 2+5
y = 7

Solution: (-2, 7)

Answer 5

y + x = 5

2x + 11 + x = 5
3x + 11 = 5
3x = -6
x = -2

y = 2 + 5
y = 7


y - 5x = -1

4x - 3 - 5x = -1
-x -3 = -1
-x = 2
x = -2

y = -10 - 1
y = -11

Answer 6

y=2x+11
y=-x+5

-x+5=2x+11
-x+x+5=2x+11+x
5=3x+11-11
-6=3x
-2=x
y=-2+5
y=3

y=4x-3
y=5x-1
5x-1= 4x-3
5x-4x-1=4x-4x-3
x-1=-3
x-1+1=-3+1
x=-2

y=5(-2)-1
y=-11