Mathematics 11.?

Question

Q1) Solve the simultaneous equations:
2x + y = 12,
3y - 2x = 56.

Q2) Simplify: { (3y^2 + 8y + 4) / y^2 - 4 }

Answer 1

The first question can solved using substitution so solving the first equation for y, y=12-2x

Plug this value for y into the second equation and you get
3(12-2x) - 2x =56
36 - 6x -2x =56
36-56=8x
x= -2.5

if x = -2.5, the in the first equation solved for y
y=12-2x=12-2(-2.5)
y=17

Checking the values using the first equation
2(-2.5) + 17 = 12

For the second equation:
3ysquared +8y+4/(y squared-4) is solved by factoring each equation.

The numeratior factors to (3y+2)(y+2)
The denominator is difference of two squares (DOTS) and factors to (y+2)(y-2)

The factors y+2 cancel so the simplified answer is
(3y+2)/(y-2)

Answer 2

Q1) add the equations together so that 2x +y +3y -2x = 12 +56, and that's 4y = 68. Solve that for y then plug it back into an equation. Solve for x.

Answer 3

2x + y = 12
-2x + 3y = 56
4y = 68
y = 17

2x + 17 = 12
2x = -5
x = -5/2


==============

3y^2 +8y +4 = (y + 2)(3y + 2)
y^2 - 4 = (y +2)(y-2)

So, cancel out the (y +2) to get (3y + 2)/(y-2)

Answer 4

Question 1
4y = 68
y = 17
2x + 17 = 12
2x = - 5
x = - 5/2

x = - 5/2 , y = 17

Question 2
(3y + 2)(y + 2) / (y - 2) (y + 2)
(3y + 2) / (y - 2)

Answer 5

2x + y = 12 ---1
3y - 2x = 56 ---2

from eqn 1,
y = 12 - 2x ---3

sub eqn 3 into 2,
3(12 - 2x) - 2x = 56
36 - 6x - 2x = 56
-8x = 56 - 36
x = -5/2
y = 12 - 2(-5/2)
y = 12 + 5
y = 17
____________________

{ (3y^2 + 8y + 4) / y^2 - 4 }

(3y^2 + 8y + 4)
(3y+2)(y+2)

y^2 - 4
y^2 - 2^2
(y+2)(y-2)

(3y+2)(y+2) / (y+2)(y-2)
(3y+2)/(y-2)

Answer 6

Q1)
Add the two equations:
2x + y = 12
-2x + 3y = 56
---------------------------
0x + 4y = 68
y = 17

Then sub y into either equation:
2x + (17) = 12
2x = -5
x = -2.5

Q2)
(3y+2)(y+2) / (y+2)(y-2)
(3y+2)/(y-2)

Answer 7

wtf! this shouldnt be THAT hard