Solve the system of equations?

Question

5x - 3y = -34
2x + 7y = -30

Answer 1

solve one for x or y and substitute:

5x - 3y = -34
so x = (3y-34)/5
now substitute

2x + 7y = -30
so
2(3y-34)/5 +7y = -30
(6y-68)/5 +7y = -30
6y-68 +35y = -150
41y = -82
y = -2
now substitute in equation
2x +7(-2) = -30
2x = -16
x = -8

Answer 2

Hello

You can solve this using the Elimination (addition), substitution, or using a Matrix.

Lets use the elimination method.

Lets multiply the top equation by 2 and the bottom equation by -5 and then add the equations.

2(5x - 3y = -34)
-5(2x + 7y = -30)

=

10x -6y = -68
-10x - 35y = 150

Lets add:
-41y = 82
y = -2.

Now plug -2 into any of the above equations to get x = -8.

So the solution is -8, -2

Hope this helps

Answer 3

5x - 3y = -34 >>>>>>>>>>>>>>>>equation 1
2x + 7y = -30 >>>>>>>>>>>>>>>>equation 2

From equation 1, 5x = -34 + 3y
x = -34 + 3y / 5 >>>>>>>>>>>>>>>>equation 3
Plug it into equation 2

2 (-34 + 3y / 5) + 7y = -30
[-68 + 6y / 5] +7y + 30 = 0
[-68 + 6y / 5] + [35y / 5] + [150 / 5] = 0>>Make denominator 5
-68 + 6y + 35y + 150 / 5 = 0
41y + 82 / 5 = 0
41y = -82 x 5
41y = -410
y = -410 / 41
y = -10

Plug y = -10 into equation 3
x = -34 + 3y / 5
x = -34 + 3(-10) / 5
x = -34 - 30 / 5
x = -64 / 5

Thus x = -64 / 5 , y = -10

Answer 4

1st equation:
5x - 3y = - 34
5x = - 34 + 3y
x = (- 34 + 3y) / 5
x = - 6.8 + 0.6y

2nd equation:
2x + 7y = - 30
2x = - 30 - 7y
x = (- 30 - 7y) / 2
x = - 15 - 3.5y

- 6.8 + 0.6y = - 15 - 3.5y
0.6y + 3.5y = - 15 + 6.8
4.1y = - 8.2
y = - 8.2 / 4.1
y = - 2

x = - 15 - 3.5(- 2)
x = - 15 + 7
x = - 8

Answer: x is - 8; y is - 2.

Proof:
5(- 8) - 3(- 2) = - 34
- 40 + 6 = - 34

2(- 8) + 7(- 2) = - 30
-16 + (- 14) = - 30
- 16 - 14 = - 30
- 30 = - 30

Answer 5

-3y = -5x-34 and 7y = -2x-30
y = (5/3)x + 34/3 and y = (-2/7)x - (30/7)

(5/3)x + 34/3 = (-2/7)x - (30/7)

Multiply everyting by 21

35x + 238 = -6x -90
41x = -328
x = -8

Set x into y
y = (5/3)(-8) + 34/3
y = -40/3 + 34/3
y = -6/3
y = -2

(-8, -2) is the answer

Answer 6

multiply the top equation by 7 and the bottom equation by 3 to cancel out the y's, it changes to

35x - 21y = -238
6x + 21y = -90

add the two equations and the y's cancel and you are left with

41x = -328

solve for x, by dividing both sides by 41 and x = -8.

Plug -8 into either equation to solve for y:
5(-8) - 3y = -34
-40 - 3y = -34, add 40 to both sides of the equal sign
-3y = 6, divide both sides of the equal sign by -3
y = -2

Answer 7

multiply the first equation by -2 and the second equation by 5 and then add the two equations to get this result:

41y=-82

this yields Y=-2

plug this into the first equation and rearrange terms to get:

5x=-40

this yields x=-8

Answer 8

solve for x or y in the first one.
plug that value for x or y into the 2nd equation.
solve for the single variable type in the equation.
plug that value into the other equation and solve.

Answer 9

last minute homework? -_-