Question

Solve the system by elimination. {2×+6y=-12; 5×-5y=10

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system using elimination, we aim to eliminate one of the variables by adding or subtracting the two equations.

First, let's multiply the second equation by 2 to make the coefficients of x in both equations the same:

2(5x - 5y) = 2(10)
10x - 10y = 20

Now, we have the two equations:

2x + 6y = -12
10x - 10y = 20

Next, we will eliminate the y variable.

Multiply the first equation by -5 and the second equation by 1:

-5(2x + 6y) = -5(-12)
10x + 30y = 60

1(10x - 10y) = 1(20)
10x - 10y = 20

Now, we have the two equations:

10x + 30y = 60
10x - 10y = 20

By subtracting the second equation from the first equation, the x variable will be eliminated:

(10x + 30y) - (10x - 10y) = 60 - 20
10x + 30y - 10x + 10y = 40
40y = 40
y = 1

Substitute the value of y back into either of the original equations, such as the first equation:

2x + 6(1) = -12
2x + 6 = -12
2x = -12 - 6
2x = -18
x = -9

The solution to the system of equations is x = -9 and y = 1.

Answer 2

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

To solve the system by elimination, we need to eliminate one of the variables by adding or subtracting the two equations.

First, let's multiply the second equation by 2 to make the coefficients of x the same in both equations:

2(5x - 5y) = 2(10)
10x - 10y = 20

Now we have the system:
2x + 6y = -12 (Equation 1)
10x - 10y = 20 (Equation 2)

Since the coefficient of x is the same in both equations, we can simply subtract Equation 1 from Equation 2:
(10x - 10y) - (2x + 6y) = 20 -(-12)

Simplifying:
10x - 10y - 2x - 6y = 20 + 12
8x - 16y = 32

We have now eliminated the variable y. Rearranging the equation:
8x = 16y + 32
8x = 16(y + 2)

Now, let's solve for x by dividing both sides of the equation by 8:
8x/8 = (16(y + 2))/8
x = 2(y + 2)

To solve for y, we can substitute the value of x in one of the original equations. Let's use Equation 1:
2x + 6y = -12

Replacing x with 2(y + 2):
2(2(y + 2)) + 6y = -12
4(y + 2) + 6y = -12
4y + 8 + 6y = -12
10y + 8 = -12
10y = -12 - 8
10y = -20
y = -20/10
y = -2

Now that we have the value of y, we can substitute it back into the equation x = 2(y + 2):
x = 2(-2 + 2)
x = 2(0)
x = 0

Therefore, the solution to the system of equations is x = 0 and y = -2.