Solve these 2 linear equations by addition?

Question

4x-6y=5
2x-3y=7

And

3x+2=16
2x-3y=-11

Answer 1

If 4x-6y is equal to 5 then 2x-3y cannot be equal to 7.There is something wrong in this equation and hence it cannot be solved

3x+2y=16...(eqn.1)
2x-3y=-11 9eqn.2)
multiplying eqn no.1 by 2 and eqn no2 by 3 we ger
6x+4y=32
6x-9y= -33
subtracting we get,13y=65
=>y=65/13=5
Putting the value of y in eqn 2,we get
2x-3*5=-11
=>2x=-11+15=4
=>x=4/2=2
Hence x=2and y=5

Answer 2

1) There is no solution as the equations are for parallel lines, not lines that intersect. You can see this by multiplying the 2nd by 2, then subtracting it from the 1st. You end up with 0 = -9 which is false. You can verify it further, but that's far enough to know.

2) Multiply the first by 2 and you get: 6x + 4 = 32. Multiply the 2nd by 3 and you get: 6x - 9y = -33. Subtract the 2nd from the 1st and you get: 9y + 4 = 65. Solving for y, you get: y = 61/9. Substitute back into the 2nd and solve for x and you get: x = 14/3.
However, it seems likely the 1st one is mis-typed and should be 3x + 2y = 16. If so, you get 6x + 4y = 32 when multiplying by 2 and the subtraction results in: 13y = 65 and so y = 5. Substitute that into either and you get x = 2.

So, either x = 14/3 & y = 61/9 OR x = 2 & y = 5.

Answer 3

4x - 6y = 5
2x - 3y = 7

To solve this by addition, we need to multiply the second equation by -2.

4x - 6y = 5
-4x + 6y = -14

Now, add the equations together.

0 = -9

The fact that we eliminate all of our variables and end up getting a false statement means this system has no solution.

2)
3x + 2y = 16
2x - 3y = -11

To solve this by addition, multiply the first equation by -2, and the second equation by 3.

-6x - 4y = -32
6x - 9y = -33

Add them together,

-13y = -65

And now, solve y as normal.
y = (-65)/(-13) = 5

Now we can obtain x. Since 3x + 2y = 16, and y = 5, then
3x + 2(5) = 16
3x + 10 = 16
3x = 6, so x = 2.

x = 2, y = 5, is the answer.

Answer 4

Simple! But I'll solve both simultaneously.
4x-6y=5
2x-3y=7
4x-6y=5 implies that x=(5-6y)/4.......(1)
2x-3y=7.......(2)
From equation (1) and (2),
2{(5-6y)/4} - 3y = 7
This implies that 2/4(5-6y)-3y = 7
0.5(5-6y)-3y=7
2.5-3y-3y=7
2.5-6y=7 This implies that 6y=7-2.5=4.5
6y=4.5 This implies that y=4.5/6=0.75
y=0.75 but x=(5-6y)/4
i.e x={5-6(0.75)}/4=(5-4.5)/4=0.5/4=0.125
Therefore x=0.125 and y=0.75

3x+2=16...(1)
2x-3y=11...(2)
From equation (1),
x=(16-2)/3=14/3=4.6061 {approximate value}
Therefore,
x=4.6061...(3)
2x-3y=11...(2)
From equation (2) and (3),
2(4.6061) - 3y = 11
9.2122 - 3y = 11
-3y = 11 - 9.2122= 1.7878
This implies that:
-3y = 1.7878
y = 1.7878/(-3)
y = -0.5959 {approximate value}
Therefore, x=4.6061 and y= -0.5959

Answer 5

1)Multiply the second equation by -2:
4x-6y=5
-4x+6y=-14
========
0x+0y=-9

No solution!

2)Multiply the first equation by 3 and the second equation by 2:
9x+6y=48
4x-6y=-22
=======
13x=26
x=2

3(2)+2y=16
6+2y=16
2y=10
y=5

The solution set is (2,5)

Check:
3(2)+2(5)=16
10+6=16
16=16

2(2)-3(5)=-11
4-15=-11
-11=-11

I hope this helps!

Answer 6

multiply first equation by -2 and the second equation by 4, then add them up. --->
-8x + 12 = -10
solve for x, and then substitute into either of the equations and solve for y.

For the second one, solve for x right away using the first equation ----> x=14/3, then substitute into the second equation for y.

Answer 7

use linear combinations