Solve by the substitution method.?

Question

Solve by the substitution method.
x - y = 15
x + y = -1

What is the solution of the system?_______
type an ordered pair.

Answer 1

x - y = 15
x + y = -1

y = -x - 1

x - (-x - 1) = 15
x + x + 1 = 15
2x = 14
x = 7

x + y = -1
7 + y = -1
y = -8

Solution: (7, -8)

Answer 2

given: x - y = 15 and x + y = -1

1. set one of the equations to y
y = -x - 1 (would be easier)

2. subsitute it into the other equation for y
x - y = 15
x - (-x - 1) = 15

3. then solve
x + x + 1 = 15
2x = 14
x = 7

4. then knowing that x = 7, you can solve for y by sticking it into the y = -x - 1 equation
y = -7 -1
= -8
or to be sure because you know x, stick it into one of the
original equations for example x + y = -1. stick in the known
x + y = -1
7 + y = -1
y = -8

Answer 3

Solve x - y = 15 for x and you get x = 15 + y. Plug this into the second equation for x and you get 15 + y + y = -1 or 15 + 2y= -1

Solve 15 + 2y = -1 for y and you get y = -8. Plug -8 into either equation for y and you can solve for x. Try the second equation. x -8 = -1 so x = 7.

Your ordered pair is the point that makes both equations true: (7, -8). Hope this helps!

Answer 4

okay so for this you just add downwards and it is easier bc the y's already have different signs..
so..

x-y=15 >the y's cancel each other out
x+y= -1
2x=14 >which means 14 /2 x =7

you place the 7 back into the first equation

7-y=15 >then you solve for y

-y=8 >subtract the 7 from both sides

y=-8 >then divide by the -1 in front of the y

so your answer is (7,-8)

Answer 5

First solve the top equation for x: x=15+y. Now substitute this into the bottom equation: (15+y)+y=-1, or 15+2y=-1....2y=-16
or y=-8. Now substitute this into either equation to get x: x-8=-1...x=7.
The solution is (7,-8)

Answer 6

Substitue 4y-2 or 6y+8 into one of the equations, whichever one you choose will be fine because it will be the same equation no matter what, just backwards. I'll try to simplify it more: eq. 1) x=4y-2 eq. 2) x=6y+8 Substitute either 4y-2 or 6y+8 into the other equation. If you use 4y-2 from eq. 1, eq. 2 would now look like this: 4y-2=6y+8 because if x is 4y-2, you can just put it right into where the x is in eq. 2 - because x IS 4y-2. It is the same for if you use 6y+8 from eq. 2 -- x IS 6y+8 so you can put this phrase into equation one where the x is because 6y+8 equals x. It would look like this - 6y+8=4y-2 Then after you have either 6y+8=4y-2 or 4y-2=6y+8, you can solve for y by adding together like terms. Using 4y-2=6y+8...... Add the 4y and 6y together by subtracting 4y from the positive 4y on the left side of the equal sign and by 6y to get 2y on the right side of the equal sign : 4y-2=6y+8 -4y -4y ^ the +4y and -4y cancels out leaving... -2=2y+8 you are trying to get y by itself, so you need to subtract 8 from the positive 8 on the right side and subtract 8 from the negative 2 on the left to get -10 on the left: -2=2y+8 -8 -8 ^ the +8 and - 8 cancels out leaving.... -10=2y To get y by itself, you need to divide the 2y by 2 (do the opposite to cancel the 2 out, like we did when it was addition/subtraction), and divide the -10 by 2: -10=2y -10/2=2y/2 ^the multiplied 2 and divided 2 cancels out leaving.... -5=y <--- -5 IS y ---- So now that you have y, you can put in -5 in either eq.1 or 2 and solve : (using eq 1): x = 4y-2 x = 4(-5)-2 x = -20-2 x = -22 ! So the ordered pair to solve these equations is (x, y) : (-22, -5)

Answer 7

x– y = 15 ------1
x + y = -1 ------2

From equation 1,
x =15 + y -----3

Substitute equation 3 into equation 2,
15 + y + y = -1
15 + 2y = -1
2y = -16

y = -8

substitute y = -8 into equation 1,
x – (-8) = 15
x + 8 = 15
x = 7

The solution is (7,-8).

Answer 8

x - y = 15
x+ y = -1
--------------
by adding
2x = 14
x = 7

>> 7 + y= -1
y = -8

{x = 7}
{y = -8}

= (7,-8)

Answer 9

x - y = 15
x = y + 15

x + y = -1
(y + 15) + y = -1
2y = -16
y = -8

x - y = 15
x - (-8) = 15
x + 8 = 15
x = 7

Answer 10

omg dont make me do math over the weekend!