need help system solving?

Question

6x + 5y = -7
2y = -1 - 3x

please, can someone help explain?

Answer 1

The second equation can be rewritten as:
3x + 2y = -1
Multiply both sides by 2
6x + 4y = -2
6x + 5y = -7 (this is the first equation)
Subtract the first equation from the second one.
y = -5
Now, plug the y = -5 into the second equation:
3x +2(-5) = -1
3x - 10 = -1
3x = 9
x = 3
So your solution is x = 3 and y = -5

Answer 2

First, rewrite the second equation in the same form as the first

6 x + 5 y = -7
3 x + 2 y = -1

Now you need to eliminate a variable: either x or y. In this case, eliminating x is easier because 6x = 2 times 3x. So, multiply the second equation by 2 to get

6 x + 5 y = -7
6 x + 4 y = -2

Now you can subtract the second from the first:

5 y - 4 y = (-7) - (-2), or y = -5.

Now substitute y = -5 into any of the equations, say the last one:
6 x + 4 y = -2 :

6 x + 4 (-5) = -2

Simplify:

6 x - 20 = -2
6 x = 20 - 2 = 18
x = 3

So the solution is x = 3, y = -5.

It is always a good idea to check the original equations, in case a mistake was made:

6 (3) + 5 (-5) = 18 - 25 = -7 is true
2 (-5) = -1 - 3 (3) is true because -10 = -1 - 9.

You can also try eliminating y by multiplying the first equation by 2 and the second by 5 and subtracting.

Answer 3

These are simultanious equations. The first step is to rearrange the 2nd equation so that it is in the same form (looks the same) as the 1st one. So we get

(1) 6x + 5y = -7
(2) 3x + 2y = -1

There are two main ways to go from here. One is to multiply equation (2) by 2. This doesn't change anything because you are multiplying both sides. So we now get:

(1) 6x + 5y = -7
(2) 6x + 4y = -2

You see now the trick is that we have obtained a 6x in both equations. Now take away equation (2) from equation (1).
x - 6x is nothing, 5y - 4y is y and -7 -(-2) is -7 +2 which is -5. The last one is tricky because you have to be really careful about getting the right signs. So we now have:

(3) y = -5

Now we go back and put this value for y into either equation (1) or (2). Let'sd use (2) so we get:

(4) 3x + (2 x -5) = -1
3x - 10 = -1
3x = -1 + 10 (added 10 to both sides)
3x = 9
x = 3

It is a very good idea to check your answers by substituting the value for x which is 3 and the value for y which -5 in the other equation. So we now check with equation (1):

6x + 5y = -7

So (6 times 3) + (5 times -5) should = -7
18 - 25 should = -7 which is true.

So ther answers are: y = -5 and x = 3

Hope this has helped you. Good luck.

Answer 4

Rearrange the second equation to find out y.

y = -1/2 - 3/2x

Now substitute waht y equals in the first equation

6x + 5 (-1/2 - 3/2x) = -7
Expand the brackets

6x -5/2 - 15/2x = -7

Multiply each term by 2 to eliminate the fractions

12x - 5 - 15x = -14
Put x terms on LHS and numbers on RHS

- 3x = - 9
Divide by -3
x = 3

Go back to equation one or two to find y
6x + 5y = -7
When x = 3
18 + 5y = -7
5y = - 25
y = 5

Answer 5

6x+5y=-7
in eqn 2,bring right hand side to left,

3x+2y=-1

multiplying eqn 2 by 2

6x+4y=-2

subtracting eqn2 from 1

y=-5
substituting for y=-5 in eqn 2 ,
3x=-1-2*-5

3x=9,
x=3

Answer 6

x = 3
y = -5