Question

Solve
2x + 3y =2/3
3x - 4y = 18

Answer 1

The system of equations is solved using the elimination method. By multiplying the equations to align the coefficients and adding them to eliminate y, x is found to be 3.3333. Plugging x back into one of the original equations then gives y as -2.0000.

Step-by-step explanation:

To solve the system of equations:

1. 2x + 3y = 2/3
2. 3x - 4y = 18

we can use the method of substitution or elimination. Let's use elimination in this case:

First, we multiply the first equation by 4 and the second equation by 3 so that the coefficients of y have the same magnitude but opposite signs:

1. (4)(2x + 3y) = (4)(2/3) → 8x + 12y = 8/3
2. (3)(3x - 4y) = (3)(18) → 9x - 12y = 54

Next, we add the two equations together to eliminate y:

8x + 12y + 9x - 12y = 8/3 + 54

17x = 54 + 8/3

17x = 54 + 2.6667

17x = 56.6667

Now we divide both sides by 17 to solve for x:

x = 56.6667 / 17

x = 3.3333

With x found, we can now substitute it back into one of the original equations to find y. We'll use the first equation for this example:

2x + 3y = 2/3

Substitute x:

2(3.3333) + 3y = 2/3

6.6666 + 3y = 2/3

3y = 2/3 - 6.6666

3y = -6.0000

Now divide both sides by 3 to solve for y:

y = -6.0000 / 3

y = -2.0000

The solution to the system is x = 3.3333 and y = -2.0000.

Answer 2

`\displaystyle [3(1)/(3), -2]`

Step-by-step explanation:

{2x + 3y = ⅔

{3x - 4y = 18

¾[3x - 4y = 18]

{2x + 3y = ⅔

{2¼x - 3y = 13½

____________

`\displaystyle (4(1)/(4)x)/(4(1)/(4)) = (14(1)/(6))/(4(1)/(4)) \\ \\`

`\displaystyle x = 3(1)/(3)`[Plug this back into both equations above to get the y-coordinate of −2];
`-2 = y`

I am joyous to assist you anytime.