Solve the system of equations by elimination
3x + 4y=31
2x - 4y=-6
(4, 5)
(5, 4)
(-5. 12.5)
(5, -4)

Explanation:

Note the matching 4y terms in each equation. The top 4y adds with the -4y down below to get 4y+(-4y) = 0y = 0. This tells us that the y terms go away entirely.

The x terms add to 3x+2x = 5x

The constants on the right hand sides add to 31+(-6) = 25

After adding the equations straight down, we end up with this new equation of 5x = 25

Dividing both sides by 5 leads to x = 5

The answer so far is between B and D.

Let's use this x value to find y

Plugging x = 5 into the first equation leads to...

3x+4y = 31

3(5) + 4y = 31

15 + 4y = 31

4y = 31-15

4y = 16

y = 16/4

y = 4

Or you could use the second equation

2x - 4y = -6

2(5) - 4y = -6

10 - 4y = -6

-4y = -6-10

-4y = -16

y = -16/(-4)

y = 4

Either way, we get the same y value when x = 5.

So x = 5 and y = 4 pair up together.

Overall, the solution is (x,y) = (5, 4)

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: