Solve each system using ELIMINATION. Remember to check! 4) 4x + y = 8 5) 3x + 5y = 54

–3x – y = 0 6x + 4y = 72

Step-by-step explanation:

Elimitation:

4) add both.

x=8. y=-24

5) multiply 2.

6x+10y=108.

subtract.

6y=36.

y=6.

x=8.

check:

4(8)-24=8. Correct.

-3(8)-24=0. correct.

3(8)+5(6)=54. Correct.

6(8)+4(6)=72 correct.

Hey there!

Given the following system:

4x + y = 8

-3x - y = 0

We do not need to change the equations at all, because the "y"s will already cancel eachother out. When we add the equations together, we get

x = 8

Now, we have to solve for y: We can do so by plugging in the value of x in to one of the equations:

4(8) + y = 8

Now we solve:

4(8) + y = 8

  32 + y = 8

           y = -24

The solution to the first given system is (8, -24)

Now, we can check by plugging the numbers into both equations, and seeing if they are true:

4(8) + (-24) = 8

 32 + (-24) = 8

                8 = 8 ~ TRUE

Now, we check the second equation:

-3(8) - (-24) = 0

 -24 - (-24) = 0

    -24 + 24 = 0

0 = 0 ~ TRUE

Both equations are true, which means that the correct solution to the first given system is (8, -24)

For the second given system, we are going to have to change one of the equations because, when added, the "x" or "y" values will not cancel out.

3x + 5y = 54

6x + 4y = 72

We can divide the second equation by -2 so the "x" values will cancel out:

-3x - 2y = -36

Now, we add the equations:

3y = 18

And solve for "y":

3y = 18

 y = 6

Now, we plug the "y" value into one of the equations and solve for "x":

3x + 5(6) = 54

 3x + 30 = 54

          3x = 24

             x = 8

The solution to the second given system is (8, 6)

Now, we can check by plugging the "x" and "y" values into both equations:

3(8) + 5(6) = 54

    24 + 36 = 54

             54 = 54 ~ TRUE

Now, we check the second equation:

6(8) + 4(6) = 72

    48 + 24 = 72

             72 = 72 ~ TRUE

Both equations are true, which means that the correct solution to the second given system is (8, 6)

Hope this helps! Have a great day, and let me know if you need more help or have questions!

10

step-by-step explanation:

7+3=10

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3