help please?

Question

1. 2x - 3y = 12
4x + 6y = 24
--------------

Solve this sytem of equations using any method and give the value of the Y value only! y = _____

2. Coincident lines have an infinite number of points in common because they are the exact same line.

true or false?

3. Which of these equations are parallel lines?

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

4x - 3y = 12
-3x + 4y = -24

3x + 4y = 12
-3x - 4y = -24

-4x + 2y = 8
¼x + ½y = 4

4. 2x + y = 8
x - y = 13

Solve this system of equations using the addition method

(2,4)

(16,3)

(7,-6)

(7,1)

Answer 1

1) y = 0.
I divided the second equation by 2 (2x + 3y = 12).

Note that
2x - 3y = 12 (first equation), and
2x + 3y = 12 (modified 2nd equation).

Since the coefficient of y makes no difference to the total, y must equal zero.

2) True.

3)
3x + 4y = 12
-3x - 4y = -24
That's the parallel line. Both slopes are -3/4.

Just switch the equations into slope-intercept form:

3x + 4y = 12
4y = -3x + 12
y = -3/4 x + 3

-3x - 4y = -24
-4y = 3x - 24
y = -3/4 x + 6

Both have the same slope (-3/4), but different y-intercepts (3 vs 6).

4)
2x + y = 8
x - y = 13

Add the two vertically:

2x + y = 8
x - y = 13
-------------------
2x + x + y - y = 13 + 8
3x = 21
x = 7

It's easier to use substitution for this step, but you can also multiply the second equation by -2 and then add to cancel out x:

2x + y = 8
x - y = 13

2x + y = 8
-2(x) -(-2)y = (-2)13

2x + y = 8
-2x +2y = -26
===========
2x - 2x + y + 2y = 8 - 26
3y = -18
y = -6
(7,-6)

Answer 2

You HS ppl seriously need to learn this stuff...