x – 4y = –7 and –3x + 5y = 0?

Question

Solve the system by addition or substitution.
x – 4y = –7
–3x + 5y = 0

I got y=-4x-11... can anyone help!

Answer 1

Addition Method:
Multiply the first equation by 3
3x - 12y = -21
Now add this to the second equation.
-7y = -21
y = 3
x - 4(3) = -7
x - 12 = -7
x = 5
Answer: (5,3)
Substitution Method:
Solve for y in the second equation.
5y = 3x
y = 3x/5
Replace y with 3x/5 in the first equation.
x - 4(3x/5) = -7
x - 12x/5 = -7
Multiply everything by 5 to get rid of the fractions.
5x - 12x = -35
-7x = -35
x = 5
y = 3x/5, so y = 3(5)/5 which means y = 3

Answer 2

You can find the unique solution to this system by doing either substitution or elimination (sometimes called linear combination).

Since it's pretty easy to write the first equation in terms of x only, lets start with that. The first equation can be written as x = 4y - 7 by just adding 4y to both sides.

Now you can substitute 4y - 7 in for x in the second equation to get:

-3(4y - 7) + 5y = 0
-12y + 21 + 5y = 0
-7y = -21
y = 3

Now plug that value for y into x = 4y - 7 to get

x = 4(3) -7
x = 12 - 7
x = 5

The solution is x = 5 and y = 3. This can also be written as the ordered pair (5,3).

The other answers that have been offered to this question that involve multiplying both sides of one equation by a constant and then adding the equations are using the elimination or linear combination method. Elimination is usually easier unless it's easy to rewrite one equation in terms of one variable at the very beginning.

Answer 3

you need to first solve for one of the variables...either x or y

So I solved for x in the first equation: x = 4y - 7

Now, since x = 4y - 7, where there is an x in the second equation you plug in what x equals: -3(4y - 7) + 5y = 0

Now, solve for y: -12y + 21 + 5y = 0

or: -7y + 21 = 0

or: -7y = -21

or: y = 3

Now where there is a y in either equation plug in the number 3 because y = 3 : x - 4(3) = -7

and now you can solve for x: x - 12 = -7

or x = 5

x = 5 and y = 3 for both equations

Answer 4

x = 4y - 7
-3(4y - 7) + 5y = 0
-12y + 21 + 5y = 0
-7y + 21 = 0
-7y = -21
y = 3

x = 4(3) - 7
x = 12 - 7
x = 5

Answer 5

if x-4y = -7 then x = 4y-7

so -3(4y-7) +5y =0
-12y +21 +5y =0
-7y= -21, so y= 3
and so x= 4(3) -7 = 5

Answer 6

By substitution:
x = 4y - 7

5y - 3(4y - 7) = 0

5y - 12y + 21 = 0

-7y = -21

y = -21 / -7 = 3

x = 4(3) - 7 = 5

You can also use this form to solve any system of two linear ecuations and two variables:

ax + by = c

dx + ey = f

x = (ce - bf) / (ae -bd)

y = (af -cd) / (ae -bd)

Answer 7

two variables, two equations.
Take the first equation and multiply it by 3 (both sides):

3x - 12y = -21

then add it to the second equation (both sides):

3x - 3x -12y + 5y = -21 + 0
-7y = -21, thus y = 3

plug y into any of the other equations to get x.

Answer 8

times top by 3
3x-12y=-21
then add the two so the x's cancel
-7y=-21
y=3
then factor into top
x-12 = -7
add twelve
x=5

Answer 9

Yeah I say X= -11

Answer 10

er... i got x= -5 and y= -3 ( i didn't use substitution or else but my calculator...)