how do you work this equation?

Question

solve by substitution

3x-4y=x-y+4
2x+6y=5y-4

I tried to work it out on scratch paper, still stumped.

Answer 1

If you move all of the like terms in one equation over to each side, then you can solve the problem. For example, the second equation becomes:

2x + 6y = 5y - 4.
y = -2x - 4. (Subtract 5y from each side and 2x from each side)

We can then substitute that into the first equation after we simplify it.

3x - 4y = x - y + 4.
2x = 3y + 4. (Subtract x and add 4y to each side)
2x = 3 * (-2x - 4) + 4. (Substitution)
2x = -6x - 12 + 4.
8x = -8.
x = -1.

And then if we substitute -1 in for x above, we get:

2x = 3y + 4.
-2 = 3y + 4.
3y = -6.
y = -2.


So x = -1, and y = -2.

Answer 2

eqn1:
3x - 4y = x - y + 4
2x - 3y = 4
2x = 4 + 3y

eqn2:
2x + 6y = 5y - 4
2x + y = -4
2x = -4 - y

set eqn 1 = eqn 2
4 + 3y = -4 - y
8 = - 4y
y = -2

substitute y = -2 into any equation (choose eqn 1)
2x = 4 + 3y
2x = 4 + 3(-2)
2x = 4 - 6
2x = -2
x = -1

therefore x = -1, y = -2

of course there are many other ways of solving this.

Answer 3

3x-4y=x-y+4
2x+6y=5y-4

Move the x's and y's to the left side
2x -3y = 4
2x +1y = -4

Subtract, to get
0x -4y = 8

Therefore, y = -2
Plug this into one of the equations, to get
2x -3(-2) = 4
2x +6 = 4
2x = 4 - 6
2x = -2
Therefore, x = -1

Check the answer back in the original equations.

Answer 4

Work it this way:

Take the first equality:
3x - 4y = x - y + 4
3x + x = 4y - y + 4
4x = 3y + 4
x = 3y/4 + 1

Plug the calue of x in the second equation:

2 (3y/4 + 1) + 6y = 5y - 4
6y/4 + 2 - 5y = -4
3y/2 - 5y = -4 -2
-7y/2 = -6
-7y = -12
y = 12/7

Plug the value of y in one of the equations:

x = 3y/4 + 1
x = 3(12/7)/4 + 1
x = 144/7 + 1
x = 152/7

Answer 5

Hai Cat C,

3x-4y=x-y+4
2x+6y=5y-4

=>
2x-3y = 4 ......(a)
2x+y = -4 ......(b)

(b)-(a) gives, 4y = -8
=> y = -2

Substituting for y in (b), we get, 2x+(-2) = -4
=> 2x - 2 = -4
=>2x = -2
=> x = -1

Answer 6

Before you do any thing you should simplify first.
The top simplifies to

5y=2x-4

and the bottom simplifies to

y=-2x-4

Now the bottom equation has been simplified for y.
1st substitute your bottom equation for y into the top and you should have

5(-2x-4)=2x-4

and now solve for x. When I did this on scratch paper I got

x=-4/3

Then take your x and plug it back into the simplified bottom equation then solve for y. after plugging this in I got

y=-4/3

So the answer would be

(-4/3, -4/3) or x=-4/3, y=-4/3

unless there is anything else that has been left out by mistake.

Answer 7

First, you COLLECT LIKE TERMS. Doing this:
2x-3y=4
2x+y =-4
Since we have "2x" in both equations, we can substitute: 2x = -(4+y) into eqtn 1. Then
-4-y-3y=4 or -4y=8 and y=-2
Then by substitution into eqtn 2" 2x-2=-4 and x=-1

Answer 8

(EQ 1):

3x - 4y = x - y + 4
2x = 3y + 4

(EQ 2)

2x +6y =5y - 4
2x + y = -4
y = -4 -2x

(EQ2) in (EQ1):

2x =3(-4 -2x) + 4
2x = -12 - 6x + 4
8x = -8
x = -1

(answer) in (EQ2):

y = -4 - 2*(-1)
y = -2

Answer 9

solving by substitution means that you need to solve for one variable, in this case the x or the y, and then "plug it in" to the second equation. im gonna start with the first equation and solve for y:
3x-4y=x-y+4 (subtract 3x)
-4y=x-y+4-3x (add y)
-4y+y=x+4-3x (combine like terms)
-3y=-2x+4 (divide by -3)
y=2/3x - 4/3

next you SUBSTITUTE this for all of the y's in the second equation and solve for x:
2x+6(2/3x - 4/3)=5(2/3x - 4/3)-4 (distribute)
2x+4x-8=10/3x - 20/3-4 (combine like terms)
6x+8/3=10/3x-32/3 (add 32/3)
6x+8/3=10/3x (subtract 8/3)
8/3=-8/3x (divide by -8/3)
x=-1

finally SUBSTITUTE -1 for all the x's in either equation to solve for y:
3(-1)-4y=(-1)-y+4 (simplify)
-3-4y=-1-y+4 (combine like terms)
-3-4y=-3-y (the -3's cancel each other)
-4y=-y (divide by -1)
y=4

FINAL ANSWER: x=-1, y=4

Answer 10

by bringing all the x n y terms on left side d equations become
2x- 3y=4, eq.1
2x+ y =- 4 eq.2

now, x=4+3y/2 from equation 1
on putin value of x in equation 2 we get

2(4+3y/2) +y = -4

or 4 +4y =-4

or y=-2

& x = -1