how do i solve this system of equations?

Question

5x+8y= -29
7x-2y= -67

Answer 1

There are different methods of doing this. The one I suggest is you solve one equation for one of it's variables and then plug it into the other. here is how it's done....

We have 5x + 8y = -29 (1st equation) and 7x - 2y = -67 (second equation) . let's solve the 2nd equation for y.
7x - 2y = -67 subtract 7x from both sides to get
-2y = -7x - 67 now divide both sides by -2 to get
y = (7/2)x + (67/2) Now let's take this and plug it back into the first equation. So we substitute the y in 1st equation with (7/2)x + (67/2). And we get
5x + 8[(7/2)x + (67/2)] = -29 now lets simplify the left side. By first distributing the 8. We get
5x + [(8*7)/2]x + [(8*67)/2] = -29 Now lets simplify some more.
5x + [4*7]x + [4*67] = -29 which gives us
5x + 28x + 268 = -29 Now first combine the x terms to get
33x + 268 = -29 Now subtract 268 from both sides, we get
33x = -297 Now divide both sides by 33 to get x by it self
x = -9 Now that we have solved for x we can plug this back into 2nd equation and solve for y. So we get
7(-9) - 2y = -67 which is equivallent to
-63 - 2y = -67 now add 63 to both sides and we get
-2y = -4 now divide by -2 to get y by it self
y = 2. So we have solved for y.

So your answer is x = -9 and y = 2. Which can also be written as (-9, 2)

If you need further clarification or more help im me or email me. Good Luck.

Answer 2

Elimination by addition method

5x + 8y = - 29- - - - - Equation 1
7x - 2y = - 67- - - - - - Equation 2
- - - - - - - - - -

Multiply equation 2 by 4

7x - 2y = - 67

4(7x) - 4(2y) = - 4(67)

28x - 8y = - 268

- - - - - - - - - - - -

Elimination of y

5x + 8y = - 29
28x - 8y = - 268
- - - - - - - - - - - -

33x = - 297

33 x / 33 = - 297 / 33

x = - 297 / 33

x = - 9

Insert the x value into eqution 1
- - - - - - - - - - - - - - - - - - - - - - - -

5x + 8y = - 29

5( - 9) + 8y = - 29

- 45 + 8y = - 29

- 45 + 8y + 45 = - 29 + 45

8y = 16

8y / 8 = 16 / 8

y = 16 / 8

y = 2

Insert the y value into the equation 1

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

5x + 8y = - 29

5(- 9) + 8(2) = - 29

- 45 + 16 = - 29

- 29 = - 29

- - - - - - - - - - -

Check for equation 2

7x - 2y = - 67

7(- 9) - 2(2) = - 67

- 63 - 4 = - 67

- 67 = - 67

- - - - - - - - - -

Both equations balance

The solution set { - 9, 2 }

- - - - - - - -s-

Answer 3

7x - 2y = -67
7x + 67 = 2y
y = 3.5x + 33.5

5x + 8y = -29
5x + 8(3.5x + 33.5) = -29
5x + 28x + 268 = -29
33x = 297
x = 9

5x + 8y = -29
5(9) + 8y = -29
45 + 8y = -29
8y = -74
y = 9.25

Answer 4

Specifically, solve the first one for x (you'll have y on the right side).

Use that right-side in the second equation, subsistuting that for x. The second equation now has no remaining x terms, but two y terms. Solve that for y.

Now go back to the first equation (or the original form of the secons equation, of you prefer). Plug in the value you just found for y. Use that to get the value of x. Q.E.D.