solving system using substitution?

Question

1. x+2y= -7
x=y+23

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

Answer 1

1.
first, substitute the second equation in for x
(y +23) + 2y = -7

then combine like terms

3y + 23 = -7
3y = -30
y = -10

Then plug that back into the original equation

x + (2)(-10) = -7
x -20 = -7
x = 13

Then you can check that it's correct by plugging it back into the other equation.

(13, -10)


2. Do the same as before

(-4y +1) + 5y = 2
y + 1 = 2
y =1

x = (-4)(1) + 1
x = -3

(-3, 1)

Answer 2

x+2y=-7
x = y+23 --> (y+23) + 2y = -7 --> 3y +23=-7 -->
3y= -30 --> y= -10
x= (-10) + 23 --> x= 13
therefore: y=-10 & x=13

2. x+5y=2
x= -4y+1 --> (-4y+1) + 5y=2 -->
y +1 =2 --> y= 1 -->
x+ 5(1) = 2 --> x + 5=2 -->
x= -3
therefore: x=-3 & y=1

Answer 3

1) x + 2y = -7, x = y + 23
substitute answer for x
(y + 23) +2y = -7 or
3y + 23 = -7 solve for y
3y = -30
y = -10 now reverse to solve for x
x = y + 23 or x = -10 + 23
x = 13

2)x + 5y = 2, x = -4y +1
-4y +1 + 5y = 2 or 5y - 4y + 1 = 2
y = 1
x = -4(1) + 1
x = -3

Answer 4

1) (y+23)+2y=-7
3y+23 =-7
-23 -23
3y = -30
3y/3 = -30/3
y = -10

x=y+23
x=-10+23
x=13

(13, -10)



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

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

(-3, 1)

Answer 5

1. substitute x=y+ 23 in the first equation
so, (y+23)+2y=-7
3y+23=-7
3y=-30
y=-10
so, x=y+23=13

2.(-4y+1)+5y=2
y+1=2
y=1
so, x=-4y+1=-3

Answer 6

For 1: You want to alter the equation to get common variables on the same side. If you subtract 2y from both sides of equation 1, you get this:
x=-2y-7
x=y+23
Therefore, you have 2 equations that can explain what x equals; therefore they equal each other:
-2y-7 = y+23
Now you can use the same method, get the common variables on the same side. Subtract y from both sides. You get:
-3y-7 = 23.
Repeat same process. Add 7 to both sides.
-3y = 30
Repeat same process. Divide by -3 both sides.
y = -10.
Now, use this result in either of your original equations:
x=y+23 becomes x = -10+23 or x = 13.

Use same method on #2.