How would I go about using the substitution method to solve this problem?

Question

-x + y = -4,
4x - 3y = 13

I think my answer is correct but I would like to clarify with what you get. Thank you in advance.

Answer 1

Solve for one variable and plug it into the second equation...

So, let's solve the first equation for y:
-x + y = -4
y = x - 4

Now plug this into the second equation:
4x - 3(x - 4) = 13

Distribute through the parentheses:
4x - 3x + 12 = 13

Subtract 12 from both sides:
4x - 3x = 1

Simplify:
x = 1

Now plug this back into your original substitution:
y = x - 4
y = (1) - 4
y = -3

So your answer is x = 1 and y = -3.

You should double-check your answer....
-x + y = -4,
-(1) + (-3) =? -4
-4 = -4 <-- check

4x - 3y = 13
4(1) - 3(-3) =? 13
4 + 9 = 13 <-- check

So your answer is:
x = 1
y = -3

Answer 2

Multiply the top equation by 3 to get
-3x +3y = -12 then add it to the bottom
x = 1 so y = -3

I'm not a fan of substitution for a problem like this

Answer 3

1) -x + y = - 4
2) 4x - 3y = 13

Solve equation 1 for y

y = x - 4

Substitute for y in equation 2

4x - 3(x - 4) = 13
4x - 3x + 12 = 13
x = 1

Put this result in equation 1

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

Check in equation 2

4(1) - 3(-3) = 13
4 + 9 = 13
13 = 13

Answer 4

-x + y = -4.......Eq 1
4x - 3y = 13.......Eq 2
Two simultaneous equations, two unknowns
Consider Eq 1.
-x + y = -4
-x = -4-y
x = 4 + y
Now substitute the value of 'x' in Eq.2
4x - 3y = 13
4(4 + y) - 3y = 13
16 + 4y - 3y = 13
16 + y = 13
y = 13 -16
y = -3
Now substitute the value of 'y' in Eq. 1 to find 'x'
-x + y = -4
-x -3 = -4
-x = -4+3
-x = -1
x= 1
(x = 1, y = -3)

Answer 5

-x + y = -4 >>>>> y = x - 4
4x - 3y = 13

subst. first to second to find x
4x - 3y = 13
4x - 3(x - 4) = 13
4x - 3x + 12 = 13
x = 13 -12
x = 1

using first eqn.
y = x - 4
y = 1 - 4
y = -3


Therefore
x = 1
y = -3

Answer 6

-x + y =-4 add x to both sides.
y= x-4
4x-3y =13 substitute in for y
4x-3(x-4) =13 multiply the brackets by -3.
4x-3x +12 =13 subtract 4 from both sides.
x =1
y=-3

Answer 7

x = y + 4
4(y + 4) - 3y = 13
4y - 3y = 13 - 16
y = -3

Substitute in first equation

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

Answer 8

First equation.

y = -4 + x

Not plug in (-4 + x) whereever u see "y" in the second equation and solve it.

Not going to do it. I'm too lazy

Answer 9

-x + y = -4
y = x - 4

4x - 3(x - 4) = 13
4x - 3x + 12 = 13
x + 12 = 13
x = 1

y = 1 - 4
y = -3

ANS : (1,-3)

Answer 10

y=-3
x=1