solve the following pairs of simultaneous equations?

Question

so i can plot them on a graph.
x=2y+4
2y-4x=2

Answer 1

If the job is to solve the system of equations graphically, I would solve the top one for y ( y = 1/2 x - 2) then graph the two on a the same set of axis.

If you wish to solve the system of equations, by substitution may be easier:

Manipulating the top equation gets you x - 4 = 2y
Note that 2y is a term in the second equation. Substitute x - 4 for 2y
x - 4 - 4x = 2
-3x - 4 = 2
-3x = 6
x = -2

Substitute the value back into the top equation:
-2 = 2y + 4
-6 = 2y
y = -3

Check your answer:
-2 = -6 + 4 (true)
-6 + 8 = 2 (also true)

Answer 2

2y - x = -4
2y - 4x = 2

x - 4 = 4x + 2
3x = -6
x = -2

Shove it back in

2y - (-2) = -4
2y + 2 = -4
2y = -6
y = -3

Answer 3

a = -1/4 and b = 5 8a + 5b = 23 12a + 3b = 12 and be simplified by dividing by 3 you get: 4a + b = 4, solve for b and you get b = 4 - 4a Put 4 - 4a in for b in the first equation and get 8a + 5(4 - 4a) = 23 8a + 20 - 20a = 23, simplify and solve for a 20 - 12a = 23 -12a = 3 a = -1/4 Now that you found a plug it back into one of the equations and solve for b.

Answer 4

substitute the first equation into the second
2y-4(2y+4)=2
2y-8y-16=2
-6y=18
y=-3
then substitute this into the first equation
x=2(-3)+4
=-6+4
=-2
the lines intersect at (-2, -3)

Answer 5

2y=x-4
2y=4x+2
___________
0=-3x-6
6=-3x
-2=x

then
2y=-8+2
2y=-6
y=-3