Question

solve

y=2/3x+6
3y+6x-18=0

Answer 1

[AI-generated answer — Step-by-Step Bot]

To solve this system of equations, you can use either the substitution method or the elimination method. Let's use the substitution method:

Step 1: Solve the first equation for y in terms of x:
y = (2/3)x + 6

Step 2: Substitute this expression for y into the second equation:
3y + 6x - 18 = 0
3((2/3)x + 6) + 6x - 18 = 0
2x + 18 + 6x - 18 = 0 (distribute 3 to (2/3)x and 6)
8x = 0
x = 0

Step 3: Substitute the value of x = 0 back into the first equation to solve for y:
y = (2/3)(0) + 6
y = 6

Therefore, the solution to the system of equations is x = 0 and y = 6.

Answer 2

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations, you can use the substitution method or the elimination method.

Using the substitution method:
1. Solve one equation for one variable in terms of the other variable.
From equation 1, solve for y:
y = (2/3)x + 6

2. Substitute the expression for y in terms of x into the other equation.
Substitute (2/3)x + 6 for y in equation 2:
3((2/3)x + 6) + 6x - 18 = 0

3. Simplify and solve for x:
2x + 18 + 6x - 18 = 0
8x = 0
x = 0

4. Substitute the value of x back into one of the original equations and solve for y:
Using equation 1:
y = (2/3)(0) + 6
y = 0 + 6
y = 6

Therefore, the solution to the system of equations is x = 0 and y = 6.

Using the elimination method:
1. Multiply equation 1 by 3 to eliminate the fractions:
3y = 2x + 18

2. Rewrite equation 2 as:
6x - 18 = -3y

3. Add the two equations together to eliminate the y-variable:
3y + 6x - 18 + 6x - 18 = 0
6x + 6x - 3y + 3y - 36 = 0
12x - 36 = 0

4. Solve for x:
12x = 36
x = 36/12
x = 3

5. Substitute the value of x back into one of the original equations and solve for y:
Using equation 1:
y = (2/3)(3) + 6
y = 2 + 6
y = 8

Therefore, the solution to the system of equations is x = 3 and y = 8.

Answer 3

[AI-generated answer — Explain Bot]

To solve these equations, we can use the method of substitution.

Let's solve the first equation for y:

y = (2/3)x + 6

Now substitute this value of y into the second equation:

3y + 6x - 18 = 0

3((2/3)x + 6) + 6x - 18 = 0

2x + 18 + 6x - 18 = 0

8x = 0

x = 0

Now substitute the value of x back into the first equation to find y:

y = (2/3)(0) + 6

y = 6

So the solution to the system of equations is x = 0, y = 6.

To check the answer, substitute these values into both equations:

For the first equation:

y = (2/3)(0) + 6 = 6, which matches the given value.

For the second equation:

3y + 6x - 18 = 3(6) + 6(0) - 18 = 18 - 18 = 0, which also matches the given equation.

Therefore, the solution is verified.