Question

Use the system of equations below to answer the questions 1-4. -2x + y = 4 2x + 3y = 20 1) Which of the following problems is created by using the elimination method on the system above? a) 4x + 4y = 24 b) 4y = 24 c) -4x + 3y = 24 d) -2y = 16 Ha a "79.4 2) Find the value of y. Show ALL of your work. O 3) Find the value of x. Show ALL of your work. W O P II search

Answer 1

To answer this question, we can proceed as follows:

1. We need to solve the next system of linear equations using the elimination method.

In this method, we can eliminate one of the variables from the system adding both equations, and previously (in some cases) multiply one of the equations by a number.

Then, we can solve this system as follows:

After adding both equations, we can eliminate the variable x. We do not need to multiply one of the equations by any number since -2x+2x = 0. We obtain a value for y after adding y + 3y = 4y, and 4 + 20 = 24. We solved the equation for y, and finally, we got y = 6.

In part 1, we have that the problem created by using the elimination method is option b:

4y = 24 (as we obtained above).

2. The value for y is given above, and this value is y = 6.

3. To obtain the value for x, we can substitute the value of y in the second equation of the given system, that is:

`2x+3(6)=20\Rightarrow2x+18=20`

To solve this equation, we can subtract 18 from both sides of the equation:

`2x+18-18=20-18\Rightarrow2x+0=2\Rightarrow2x=2`

Finally, to find the value for x, we need to divide both sides of the equation by 2:

`2x=2\Rightarrow(2x)/(2)=(2)/(2)\Rightarrow x=1`

In summary, we have that the values for x = 1, and for y = 6, using the elimination method above.