Find the values of and that solve the following system of equations:?

Question

-3x + 4y = -4
7x - 3y = 22

solve for x and y

Answer 1

-9x+12y=-12 (1)*3
28x-12y=88 (2)*4
adding
19x=76
x=76/19
=4
substituting in
-3x+4y=-4
-12+4y=-4
4y=-4+12
y=8/4
=2
so x=4 andy=2

Answer 2

lets do it by substitution. In the first eq. yo have that x=(4+4y)/3 subtstituing this in the second equation u have 7(4+4y)/3-3y=22 multiplyang both side by 3 you have 7(4+4y)-9y=22 then you have that 21y=-6 so y=-2/7 and substituing this value in eq. 1 yo have that x=(4+4*(-2/7))/3=4/3-4/3(2/7)=20/21

Answer 3

take from the first equation
-3x = -4 - 4y
x = (4+4y)/3

then substitute this into the second equation
7(4+4y)/3 - 3y = 22
28 + 28y - 9y = 66
19y = 38
y = 2

then substitute y = 2 into any equation to solve for x

x = (4+4y)/3
x = (4 + 8) /3
x = 4

Answer 4

There are two methods you can use:
(1) Elimination. Multiply each equation by a certain number, subtract equations, and eliminate one variable to solve for the other.
(2) Substitution. Solve for one variable, and then plug it in to the other equation.

I'm going to use elimination.

First, I'm going to multiply the first equation by 7, and the second equation by 3. The two equations then become

-21x + 28y = -28
21x - 9y = 66

Now, I'm going to ADD these two equations together (as per elimination).

(-21x + 28y) + (21x - 9y) = (-28 + 66)

The -21x and the 21x should cancel out, leaving us with

28y - 9y = -28 + 66
19y = 38
y = 2

Since we have one variable, we can solve for the other one by plugging in y = 2 for any equation. Let's use the second one.

7x - 3(2) = 22
7x - 6 = 22
7x = 28
x = 4

Therefore, x = 4 and y = 2 is the solution.

Answer 5

substitute one variable in terms of the other
let's use the bottom equation
7x-3y=22... simply get x by itself on one side
7x= 22+3y
x= (22+3y)/ 7

now for that value of x substitute it into the first equation where x is
-3 ((22+3y)/7) +4y=-4

now just solve that for y and you will get a value for y as a number
then just plug it back into any equation to get a value for x .

Answer 6

-3x +4y = -4 ...(a)
7x - 3y = 22 ...(b)

(a)*7: -21x + 28y = -28 ...(c)
(b)*3: 21x - 9y = 66 ...(d)

(c)+(d): 19y = 38, y = 2 --> put it back to (a), -3x = -4 - 8= -12, x=4

x=4 and y=2