Solve the system of equations by the substitution method.?

Question

{-7x + y = -8
{-8x - 4y = -4

a. (-1, 1)
b. (2, -2)
c. (1, -1)
d. no solution

Answer 1

C.

-7x + y = -8, so y = 7x - 8.
-8x - 4(7x-8) = -4
-8x - 28x + 32 = -4
-36x = -36
x = 1
y = -1

Answer 2

Isolate the y in the first equation. So 7x-8 = y Then substitute that in for y in the 2nd equation, so you have -8x -4(7x-8) = -4.

Now you need to multiply the 4 through
-8x-28x+32 = -4.

Now combine the x's.
-36x + 32 = -4.

Put the 32 on the other side.
-36x = -36

divide by -36
x = 1

Put this back into the first equation
-7(1) + y = -8
-7 + y = -8

Move the -7 to the other side.
y=-1

So your solution is x=1, y= -1

The answer is C.

Answer 3

Math test tip:
You could solve the system by substitution, but that takes longer than substituting the answers in a, b & c into the two equations and seeing which one (if any) satisfies both equations. The answer is c -- I did that in about 10 seconds in my head -- versus about 2 minutes doing it on paper. OF COURSE, if you math teacher checks your work or gives you partial credit for incorrect solutions, you will want to do it long hand:

STEP 1 -- solve for one variable in terms of the other in one of the equations:

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

STEP 2 -- plug that form of the variable into the OTHER equation

-8x - 4y = -4
-8x -4(7x - 8) = -4......distribute the -4 to get:
-8x - 28x + 32 = -4..... combine like terms, -32 from both sides:
-36x = -36 .................. divide both sides by -36
x = 1

STEP 3: plug that value into one othe other equations and solve for the second variable

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

The answer is c --- YOU SHOULD CHECK YOUR WORK BY PLUGGING (1,-1) INTO BOTH EQUATIONS TO VERIFY THAT (1,-1) SATISFIES THEM BOTH. I already did that when I used my Math Test Tip above.

Good Luck!

Answer 4

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

- 8x - 4y = - 4
4y = 4 - 8x
y = 1 - 2x

Find x:
7x - 8 = 1 - 2x
9x = 9
x = 1

Find y:
= 7(1) - 8
= 7 - 8
= - 1

Answer: c. (1, - 1)

Proof:
- 8(1) - 4(- 1) = - 4
- 8 + 4 = - 4

Answer 5

y = -8 + 7x
-8x -4y = -4
-2x -y = -1
2x + y = 1
2x + -8 + 7x = 1
9x - 8 = 1
9x = 9
x = 1
-2 -y = -1
y = -1

c) (1, -1)

Answer 6

y = 7x - 8
- 8x -4(7x - 8) = - 4
- 36x + 32 = - 4
- 36x = - 36
x = 1

-7 + y = - 8
y = - 1

x = 1 , y = - 1
OPTION c

Answer 7

y=-1,x=1

so answer is "C"