Question

solve the system of equations

3x+y=2
7x-4y=30

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations:

1) Start by multiplying the first equation by (-4) to eliminate the y variable:

-4(3x + y) = -4(2)
-12x - 4y = -8

2) Next, set up the second equation and the result of step 1 to create a new system of equations:

-12x - 4y = -8
7x - 4y = 30

3) Subtract equation 1 from equation 2:

(7x - 4y) - (-12x - 4y) = 30 - (-8)
7x + 12x - 4y + 4y = 30 + 8
19x = 38

4) Divide both sides of the equation by 19:

x = 38/19
x = 2

5) Substitute the x value of 2 into either of the original equations:

3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4

6) Therefore, the solution to the system of equations is x = 2 and y = -4.

Answer 2

[AI-generated answer — Explain Bot]

To solve this system of equations, there are several methods you can use, such as substitution, elimination, or graphing. I'll explain how to solve it using the substitution method step by step.

Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation for y:
3x + y = 2
y = 2 - 3x

Step 2: Substitute the expression for y in the second equation.
Now, replace y in the second equation with the expression we found in step 1:
7x - 4(2 - 3x) = 30

Simplifying the equation further:
7x - 8 + 12x = 30
19x - 8 = 30

Step 3: Solve the resulting equation for x.
To isolate x, we'll add 8 to both sides of the equation:
19x = 30 + 8
19x = 38

Divide both sides by 19:
x = 38/19
x = 2

Step 4: Substitute the value of x back into either of the original equations to solve for y.
Using the first equation:
3(2) + y = 2
6 + y = 2

Subtract 6 from both sides of the equation:
y = 2 - 6
y = -4

Step 5: Check the solution by substituting the found values back into both original equations.
Using the first equation:
3(2) + (-4) = 2
6 - 4 = 2
2 = 2 (True)

Using the second equation:
7(2) - 4(-4) = 30
14 + 16 = 30
30 = 30 (True)

Both equations are satisfied by the values x = 2 and y = -4. Therefore, the solution to the system of equations is x = 2 and y = -4.

Answer 3

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

To solve the system of equations:

Step 1: Multiply the first equation by 4 to eliminate y.
4(3x + y) = 4(2)
12x + 4y = 8

Step 2: Add the two equations together to eliminate y.
(12x + 4y) + (7x - 4y) = 8 + 30
12x + 4y + 7x - 4y = 38
19x = 38

Step 3: Divide both sides of the equation by 19 to solve for x.
x = 38 / 19
x = 2

Step 4: Substitute the value of x (which is 2) back into one of the original equations to solve for y. Let's use the first equation.
3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4

So the solution to the system of equations is x = 2 and y = -4.