solve the system by elimination. Check your solution. −2x − 5y = 9 3x + 11y = 4

Answer 1

-2x -5y = 9 .........equation 1

3x + 11y = 4 ...... equation 2

To solve the system by elimination, we need to eliminate one of the variables. We can do this by multiplying one or both of the equations by a constant such that the coefficients of one of the variables (in this case x) are opposites.

Let's multiply equations 1 by 3 and equation 2 by 2:

3 (-2x -5y = 9) = -6x -15y = 27 ... equation 3

2 (3x +11y = 4) = 6x +22y = 8 ...... equation 4

Now, let's add both equations to eliminate the x - variable:

(-6x -15y) + (6x + 22y) = 27 + 8

-6x + 6x -15y + 22y = 35

7y = 35 (divide both sides by 7)

y = 5

Substitute y = 5 in equation 1

-2x - 5(5) = 9

-2x - 25 = 9

-2x = 9 + 25

-2x = 34 ( divide both sides by -2)

x = -17

thus, the solution to the system is x = -17 and y = 5

To check:

Substitute x = -17 and y = 5 into the original equations:

-2 (-17) - 5 (5) = 9

34 - 25 = 9

9 = 9

and

3 (-17) +11(5) = 4

-51 + 55 = 4

4 = 4

Answer 2

-2x-5y=9

3x+11y=4

Multiply the first equation by 3 and the second equation by 2:

-6x-15y=27

6x+22y=8

(This keeps the coefficients smaller than when eliminating y, and thus, mor manageable.)

Add them:

7y=35

Divide by 7:

y=5

Substitute in the first equation:

-2x-5(5)= -2x-25=9

Add 25 to both sides:

-2x=9+25=34

Divide both sides by -2:

x=-17

Check by substituting into the second equation:

3(-17)+11(5)=-51+55=4 which checks out.

Answer 3

So, we have two equations:

-2x - 5y = 9

3x + 11y = 4

In order to solve by elimination we want to have one of the variables be eliminated by either adding or subtracting the equations. For example, 6x - 6x would cancel out, or 6x + (-6x) would cancel out. So, our goal to start is to get the coefficients for one of the variables to be the same or opposites. I am going to choose to use the x-variable here.

We have a -2x and 3x. We can multiply the first equation by 3 to get a -6x and the second equation by 2 to get a 6x.

So,

3(-2x -5y = 9)

When you distribute the 3 you get

-6x - 15y = 27

and for the second equation:

2(3x+11y = 4)

When you distribute the 2 you get:

6x + 22y = 8

Now our 2 equations are -6x - 15y = 27 and 6x + 22y = 8.

We have a situation where the coefficients of a variable are opposite so we can add the equations to get rid of this variable.

-6x - 15y = 27

+

6x + 22y = 8

=

7y = 35

y = 5

Now that we know y, we can plug that into either equation to get x. I chose to use the first equation.

-2x - 5y = 9

-2x - 5(5) = 9

-2x - 25 = 9

-2x = 34

x = -17

So the final answer is x=-17 and y=5