Can anyone solve two problems?

Question

1. 4X + Y = 16 ; 2X + 3Y = 24

2. 12X + Y = 25 ; 8X - 2Y = 14

Answer 1

4x +y = 16 ;2x + 3y = 24 Multiply the 2nd with -2, that gives -4x -6y = -48 Add the two: 0x - 5y = -32
Division by -5 gives y = 6,4
Insert this value into the first equation: 4x + 6,4 = 16
4x = 9,6 ; x = 2,4

Number 2 is even easier:
Multiply the first equation by 2 and add the equations.
24x + 2y = 50 plus 8x - 2y = 14 gives 32x = 64; x = 2
You can now choose: 24 + y = 25 or 16 - 2y = 14
(That you get when you replace in the original equations
x by 2) Anyhow you'll find y = 1

Answer 2

Confirming the first answer.

1. Transfrom first equation y=16-4x. Fit into second equation: 2x+3*(16-4x)=24 -> 2x+48-12x=24 -> -10x=-24 ->x=2.4. Then y=16-4*2.4=6.4
So x=2.4, y=6.4.

2. Similar to 1.:
y=4x-7. Entered in first equation: 12x+4x-7=25 -> 16x=32 ->x=2; y=4*2-7=1
So x=2, y=1

Answer 3

Solve by using system of equations. For number one, multiply the first equation by -3 so that the Y's will cancel out and you can solve for X. Plug in your answer for X into one of the equations and solve for Y. X = 2.4 and Y = 6.4

For number similar. Multiply the first equation by 2 so you can cancel out the y's and get a value for X. Subsitute your X value into one of the equations and you should get your Y value. X=2 and Y = 1

Answer 4

1. 4X + Y = 16 ; 2X + 3Y = 24

multiply first equation by three;
=>12x+3y=48
subtract one from the other to get;
10x=24
x=2.4
put that into one of the above and rearrange for y to get y=6.4




2. 12X + Y = 25 ; 8X - 2Y = 14
multiply first on by 2;
=>24x+2y=50
add to the other one to get;
32x=36
so x=1.125
and put x into one of the above to get y by rearrangment again;
I get y=-11.5

Answer 5

1. x = 2.4 , y = 6.4

2. x = 2 , y = 1