Question

Solve for x and y.

2x + 3y = 23
3x – y = 7

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for x and y, we can use the method of substitution or elimination.

Method 1: Substitution
We can solve one equation for x or y and substitute it into the other equation.

From the second equation, isolate y:
3x - y = 7
y = 3x - 7

Substitute y into the first equation:
2x + 3(3x - 7) = 23
2x + 9x - 21 = 23
11x - 21 = 23
11x = 44
x = 4

Substitute x = 4 into the second equation to solve for y:
3(4) - y = 7
12 - y = 7
-y = 7 - 12
-y = -5
y = 5

The solution to the system of equations is x = 4 and y = 5.

Method 2: Elimination
Multiply the first equation by 3 and the second equation by 2 to make the coefficients of y in both equations equal:

6x + 9y = 69 (equation 1)
6x - 2y = 14 (equation 2)

Now subtract equation 2 from equation 1 to eliminate x:
(6x + 9y) - (6x - 2y) = 69 - 14
6x + 9y - 6x + 2y = 55
11y = 55
y = 5

Substitute y = 5 into equation 2 to solve for x:
3x - 5 = 7
3x = 7 + 5
3x = 12
x = 4

The solution to the system of equations is x = 4 and y = 5.

Answer 2

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

To solve for x and y in the system of equations:

2x + 3y = 23
3x - y = 7

Step 1: Choose one of the equations and isolate one of the variables. Let's isolate y in the second equation.
3x - y = 7
Add y to both sides:
3x = y + 7

Step 2: Use the isolated variable in the other equation. Substitute y + 7 for y in the first equation.
2x + 3(y + 7) = 23
Distribute 3:
2x + 3y + 21 = 23

Step 3: Simplify the equation.
2x + 3y + 21 = 23
Combine like terms:
2x + 3y = 2

Step 4: Now we have a system of equations in terms of x and y:
2x + 3y = 2
3x - y = 7

Step 5: We can solve this system of equations using the method of substitution or elimination.
Let's use the method of substitution.
From our second step, we have 3x = y + 7.
We can substitute this value into the first equation.

2x + 3y = 2
2x + 3(y + 7) = 2
Distribute 3:
2x + 3y + 21 = 2
Combine like terms:
2x + 3y = -19

Step 6: Now we have a new system of equations:
2x + 3y = -19
3x - y = 7

Step 7: Use the new system of equations to solve for x and y.
We can use the method of elimination to eliminate either x or y. In this case, let's eliminate x:

Multiply the first equation by 3:
6x + 9y = -57
Multiply the second equation by 2:
6x - 2y = 14

Subtract the second equation from the first equation:
(6x + 9y) - (6x - 2y) = (-57) - (14)
6x - 6x + 9y + 2y = -57 - 14
11y = -71
Divide both sides by 11:
y = -71 / 11
y = -6.45 (rounded to two decimal places)

Step 8: Substitute the value of y back into one of the original equations to solve for x. Let's use the second equation:
3x - y = 7
3x - (-6.45) = 7
3x + 6.45 = 7
Subtract 6.45 from both sides:
3x = 0.55
Divide both sides by 3:
x = 0.55 / 3
x = 0.18 (rounded to two decimal places)

Step 9: The solution to the system of equations is x = 0.18 and y = -6.45.