Question

Solve the system of equations

5x+2y=14
x-6y=22

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Using the method of substitution:
We can solve the second equation for x in terms of y:
x = 22 + 6y.

Now we substitute this expression for x into the first equation:
5(22 + 6y) + 2y = 14.
Distribute the 5:
110 + 30y + 2y = 14.
Combine like terms:
32y + 110 = 14.
Subtract 110 from both sides:
32y = -96.
Divide both sides by 32:
y = -3.

Now substitute this value of y back into the second equation to solve for x:
x - 6(-3) = 22.
Multiply:
x + 18 = 22.
Subtract 18 from both sides:
x = 4.

The solution to the system of equations is x = 4 and y = -3.

Answer 2

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

To solve the system of equations, we can use the method of substitution or elimination. Let's use the substitution method.

Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the second equation for x:

x - 6y = 22
x = 6y + 22

Step 2: Substitute the expression for x in terms of y into the other equation.

5x + 2y = 14
5(6y + 22) + 2y = 14
30y + 110 + 2y = 14
32y + 110 = 14

Step 3: Move the constant term to the other side of the equation.

32y = 14 - 110
32y = -96

Step 4: Divide both sides of the equation by the coefficient of y.

y = -96/32
y = -3

Step 5: Substitute the value of y into the first equation to solve for x.

5x + 2(-3) = 14
5x - 6 = 14
5x = 20
x = 4

So the solution to the system of equations is x = 4 and y = -3.

Answer 3

[AI-generated answer — Explain Bot]

To solve this system of equations, you can use the method of substitution or the method of elimination. I'll guide you through both methods so you can choose the one you prefer.

Method 1: Substitution
Step 1: Solve one equation for one variable.
Let's solve the second equation for x.
x - 6y = 22
x = 22 + 6y

Step 2: Substitute the expression for x into the other equation.
Now substitute x with the expression we found in the first equation.
5x + 2y = 14
5(22 + 6y) + 2y = 14

Step 3: Simplify and solve for y.
Distribute 5 to the terms inside the parentheses.
110 + 30y + 2y = 14

Combine like terms.
110 + 32y = 14

Subtract 110 from both sides.
32y = 14 - 110
32y = -96

Divide both sides by 32 to isolate y.
y = -96 / 32
y = -3

Step 4: Substitute the value of y into either one of the original equations to find x.
Let's substitute y = -3 into the first equation.
5x + 2(-3) = 14
5x - 6 = 14

Add 6 to both sides.
5x = 14 + 6
5x = 20

Divide both sides by 5 to isolate x.
x = 20 / 5
x = 4

The solution to the system of equations is x = 4 and y = -3.

Method 2: Elimination
Step 1: Multiply one or both equations by appropriate constants to make the coefficients of one variable opposite in sign.
Let's multiply the second equation by 5 to make the coefficients of x opposite.
5(x - 6y) = 5(22)
5x - 30y = 110

We now have the following system of equations:
5x + 2y = 14
5x - 30y = 110

Step 2: Add or subtract the equations to eliminate one variable.
Subtract the first equation from the second equation.
(5x - 30y) - (5x + 2y) = 110 - 14
5x - 30y - 5x - 2y = 96
-32y = 96

Step 3: Solve for the remaining variable.
Divide both sides by -32 to isolate y.
y = 96 / -32
y = -3

Step 4: Substitute the value of y into either one of the original equations to find x.
Let's substitute y = -3 into the first equation.
5x + 2(-3) = 14
5x - 6 = 14

Add 6 to both sides.
5x = 14 + 6
5x = 20

Divide both sides by 5 to isolate x.
x = 20 / 5
x = 4

The solution to the system of equations is x = 4 and y = -3.

Both methods yield the same solution: x = 4 and y = -3.