Solve using substitution or elimination. Remember, you must check your work.10x -15y = 10
4x + 6y = 0

Answer:

The answer to your question is: (1/2, -1/3)

Step-by-step explanation:

Elimination

                           10x - 15y = 10    (I)

                             4x + 6y = 0     (II)

Multiply (I) by 2 and (II) by -5

                          20x - 30y = 20

                         -20x - 30y = 0

                                                                Add both equations

                           0   - 60y = 20

                                       y = -20/60

                                      y = - 1/3

Substitute y in (II)

                          4x + 6(-1/3) = 0

                          4x - 2 = 0

                          4x =  2

                            x = 2/4

                           x = 1/2                      

                4(1/2) + 6(-1/3) = 0

                     4/2 - 6/3 = 0

                      2 - 2 = 0

                            0 = 0          

Answer:

(1/2, -1/3)

Step-by-step explanation:

To solve using elimination, you have to make one of the variables from both equations additive inverses. Let's make the x-variables additive inverses.

First, we multiply the first equation by -2.

-2(10x - 15y) = -2(10)

-20x + 30y = -20

Now, we muliply the second equation by 5.

5(4x + 6y) = 0

20x + 30y = 0

If you look at the x-variables, now they are additive inverses. Now we add the two equations together.

-20x + 30y = -20

20x + 30y = 0

60y = -20

/60       /60

y = -1/3

Now you plug in the known y-value into any of the first equations. Let's use 4x + 6y = 0

4x + 6(-1/3) = 0

4x - 2 = 0

+2         +2

4x = 2

/4     /4

x = 1/2

The solution to this system of equations is (1/2, -1/3). You can change to decimal form if you want. To check your work, you plug in the x and y-values into the two equations in the question.

10x - 15y = 10

10(1/2) - 15(-1/3) = 10

5 + 5 = 10

10 = 10

So, the solution is true for this equation. Let's check the second one.

4x + 6y = 0

4(1/2) + 6(-1/3) = 0

2 - 2 = 0

0 = 0

Yes! When you plug the solution into the equations, they are true! So, your solution is (1/2, -1/3).