what i need answered

Question

Solve the system -16y = 22 + 6x and -11y - 4x = 15. Write your answer as a coordinate point.

Answer 1

divides first equation by 2

-8y = 11 + 3x and -11y - 4x = 15

adds 8y to first equation and changes the sign of the second equation:

-11 = 3x + 8y and 4x + 11y = -15

stacks them to make 2 by 2 system:

3x + 8y = -11

4x + 11y = -15

-4 times top equation and 3 times bottom equation:

-12x + -32y = 44

12x + 33y = -45

adds them together:

y = -1

substitutes into the 2 by 2 system:

3x + 8y = -11 ---> 3x + -8 = -11 --> 3x = -3 ---> x = -1

4x + 11y = -15 --> 4x + -11 = -15 ---> 4x = -4 ---> x = -1

(-1, -1) is the solution

Answer 2

Hi Kaitlin,

This is a how to guide to help:

1. Look at your equations to see if you can simplify one to get smaller numbers. This makes it easier to work with and you're less likely to make math errors (frustrating when you're algebra is correct but you get the question wrong due to a math error).

-11y - 4x = 15 This one is as simple as it's going to get

-16y = 22 + 6x All terms here are divisible by 2. Okay as long as you do it to ALL the terms

2 2 2

-8y = 11 + 3x Simplified

1. Look at your equations and make sure all the terms are lined up in the exact same order and everything is on the correct side of the equal sign. It doesn't matter what order it is, as long as it's the same.

-11y - 4x = 15

-8y = 11 + 3x x-term is on the wrong side so move it keeping your eq. balanced

-3x -3x

-8y - 3x = 11

1. Stack your equations lining up the terms: (which one goes on top/bottom doesn't matter)

-11y - 4x = 15

-8y - 3x = 11

1. Look at your terms. You want either the x-term or the y-term to cancel out. You could use either but the 3 and the 4 on the x-term is going to be easier mathematically. The smallest number 3 and 4 go into is 12. Since they need to cancel out, you must have opposite signs. Again, it doesn't matter which x-term is +/- but they need to be opposites. Be sure to distribute to all terms in your equation.

3(-11y - 4x = 15) -4(-8y - 3x = 11)

-33y - 12x = 45 32y + 12x = -44

1. Now stack your system (again the order doesn't matter top/bottom) making sure your terms line up. Combine your two equations and simplify to solve for one of your variables:

-33y - 12x = 45

32y +12x = -44

-1y = 1

-1 -1

y = -1 This is just your y-term, you still need to find x

1. Use your y-value in one of your equations (doesn't matter which) and solve for x:

-11y - 4x = 15

-11(-1) - 4x = 15

11 - 4x = 15

-11 -11

-4x = 4

-4 -4

x = -1

*Now write your solution as an ordered pair (x,y): (-1, -1)

**As a test taking strategy to check your work, you should be able to take your ordered pair, plug it back into both of the original equations and get true statements for both:

-11y - 4x = 15 -16y = 22 + 6x

-11(-1) - 4 (-1) = 15 -16(-1) = 22 + 6(-1)

11 - (-4) = 15 16 = 22 + (-6)

11 + 4 = 15 16 = 22 - 6

15 = 15 Check! 16 = 16 Check!