Question

Solving systems equations by elimination

-2x-9y=-25
-4x-9y=-23



x-y=11
2x+y=19




-4x-2y=-12
4x+8y=-24





5x+y=9
10x-7y=-18

Answer 1

To solve the system of equations by elimination, we can eliminate either x or y by adding or subtracting the equations. After eliminating one of the variables from the first two equations and the next two equations, we are left with a new system of equations involving x and y. Solving this new system, we find that x = 3 and y = -2.

Step-by-step explanation:

To solve the given system of equations by elimination, we need to eliminate one variable by adding or subtracting the equations. Let's start by eliminating one of the variables from the first two equations. We can multiply the second equation by 2 to obtain -8x - 18y = -46. Now, we can add this equation to the first equation to eliminate y. This gives us -2x - 9y -8x - 18y = -25 -46.

Simplifying this further, we get -10x - 27y = - 71. Now, let's eliminate the same variable, y, from the next two equations. We can multiply the fourth equation by 2 to obtain 4x + 2y = 12. Adding this equation to the third equation, we get x - y + 4x + 2y = 11 + 12, which simplifies to 5x + y = 23.

Now, we have a system of two equations with two variables: -10x - 27y = -71 and 5x + y = 23. We can solve this system by substitution or elimination methods. By solving them, we find that x = 3 and y = -2.

Answer 2

I won't answer them all for you (don't want to cheat - need to learn something).
But for the first one given:

-2x-9y=-25
-4x-9y=-23

you set up either x or y (which ever one you want to eliminate) so that one of them cancels.
So this one is easy - you just have to multiply an entire row by negative (doesn't matter which one) - so that the y's will be + and -

Since they're both 9 and they're subracting NOW - you can eliminate the y value. Now add/subtract the x's. So it'd be -2 or 2 depending on how you eliminated y. Then add the number outside of the = sign. Now just solve for x. After that plug in whatever you got for x into both of the rows. Then find the y value.

Hopefully this wasn't confusing -- reply if it is and I will try to simplify. I can give you contact if you need help with the rest

Good luck!