Solve the system by addition or substitution.?

Question

3x – 4y = 8
6x – 2y = 10
I dont get this, can someone help me

Answer 1

3x – 4y = 8
(-2)(6x – 2y) = (-2)10

3x – 4y = 8
-12x + 4y = -20

Add the two equations and you get:
-9x = -12
x=12/9 = 4/3

Solve for y:
3x – 4y = 8, -4y=8-3x
y=(8-3x)/-4

Substitute 4/3 for x
y=(8-3(4/3))/-4 = -1

Therefor:
x=4/3
y=-1

Answer 2

Solve by addition. Multiply one or both equations by some number (not necessarily the same number for both equations) so that the co-efficients of x, or those of y, are opposites. For example, in this one system I found online,[1]

x - 2y = 14
x + 3y = 9

just invert the first (or second, but I'll do the first) equation to read

-x + 2y = -14
x + 3y = 9.

Add:

5y = -5 (the x's went away); so y = -1.

Thus, since x - 2y = 14, then x - 2(-1) = 14, or x+2 = 14, so x=12.

(If it's easier on you, just subtract one from the other.)

Alternatively, triple the first equation and double the second, to read

3x - 6y = 42
2x + 6y = 18,

to get rid of the y's. Now add, and get 5x = 60, so that x = 12. And x - 2y = 14, so 12 - 2y = 14. Solve for y and get that y = -1.

If you prefer, solve by substitution. Solve one equation for x (or y) and get something like, x = 11y + 1/7, or whatever. Substitute this for x in the other equation, and solve that for y. Now you know y. Get x the same way as above, substituting the value of y into either equation and solving.

Hope that helps,

Answer 3

1) x =4 y=1
2) x=2 Y=1

Answer 4

3x - 4y = 8 - - - - - - - Equation 1
6x - 2y = 10 - - - - - - Equation 2

- - - - - - - - - - -- - - - - - - -

Multiply -2 for equation 2

-2(6x) - (-2)(2y) = -2(10)

-12 + 4y = - 20

new equation 2

- - - - - - - - - - - - - - - - - - - - - -

3x - 4y = 8
-12x + 4y = - 20
- - - - - - - - - - -

- 9x + 0 = - 12

- 9x = - 12

- 9x/- 9 = -12/- 9

x = 4/3

The answer is x = 4/3

The solution ser is { 4/3 }

Insert the x value into the equation 1

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

Solving for y equation 1

3x - 4y = 8

3(4/3) - 4y = 8

12/3 - 4y = 8

4 - 4y = 8

4 - 4y - 4 = 8 - 4

- 4y = 4

- 4y/-4 = 4/- 4

y = - 1

The answer is y = -1

The solution set is { - 1 }

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

3x - 4y = 8

3(4/3) - 4(- 1) = 8

12/3 + 4 = 8

4 + 4 = 8

8 = 8

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

Check fkor equation 2

6x - 2y = 10

6(4/3) - 2(- 1) = 10

24/3 + 2 = 10

8 + 2 = 10

10 = 10

- - - - - - - - - - - - - - - - - - - -

The solution set is { 4/3, -1 }

Answer 5

well, you could do it this way:

you multiply the top equation by 2 so that it becomes 6x - 8y = 16. then you multiply the bottom equation by -4 so that it becomes -24x + 8y = -20. Then the -8y and +8y cancel out, so that the equations become 6x = 16 and -24 = -20. solve one of the equations for x, and substitute that x value in the other equation, and you get y. you now have your x and y value.
after doing that, your answer will be (4/3, -1).

hope this helps :-)

Answer 6

You must choose to either eliminate one variable by getting both coefficients the same and subtracting, or getting the coefficients to be opposites of each other and adding. I always prefer to add...less chance to make errors.

I will choose to multiply the first equation by -2, then add

-6x+8y=-16
6x-2y=10

6y=-6
y=-1
now put -1 in for y in either equation and solve for x

3x -4(-1)=8
3x+4=8
3x=4
x=4/3

Check both in the other equation.

Answer 7

3x - 4y = 8
6x - 2y = 10

6x - 2y = 10
-2y = -6x + 10
y = 3x - 5

3x - 4(3x - 5) = 8
3x - 12x + 20 = 8
-9x + 20 = 8
-9x = -12
x = (4/3)

y = 3(4/3) - 5
y = 4 - 5
y = -1

ANS : ((4/3),-1)

Answer 8

3x-4y=8-----(1)
6x-2y=10-----(2)
multiply eqn (1) by 2 and multiply eqn (2) by 4
we get
6x-8y=16
24x-8y=40
now subtract these two eqns
we get
6x-8y-24x+8y=16-40
-18x=-24
x=4/3=1.333

now put value of x in either eqn (1) or (2) to calculate value of y
using in eqn(1)
3(4/3)-4y=8
4-4y=8
4y=-4
y=-1

hence x=4/3, y=-1

Answer 9

You replace "y" for "x+a million" in the equation 4x-3y=0. a million). 4x - 3(x+a million) = 0 then you particularly distribute. 2). 4x - 3x - 3 = 0 upload the 4x and -3x. 3). x - 3 = 0 Use the addition property of equality. 4). x = 3 replace "x" in the equation y = x+a million to discover "y" 5). y = 3+a million upload. 6). y = 4

Answer 10

-2* [3x – 4y ]= -2* [8 ] then :
-6x+8y = -16
6x – 2y = 10
add them :
6y = -6 so y= -1
then :
6x – 2y = 10 -->> y= -1 -- >> 6x + 2 = 10 so 6x=8 -->> x = 8/6

that`s it ;-)