Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system using elimination, we can multiply the first equation by 5 and the second equation by 2 to get the same coefficient for x:

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

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

Now, we can subtract the second equation from the first equation to eliminate the x term:

(10x + 30y) - (10x - 10y) = -60 - 20
10x + 30y - 10x + 10y = -80
40y = -80
y = -80/40
y = -2

Now, substitute the value of y back into one of the original equations:

2x + 6(-2) = -12
2x - 12 = -12
2x = 0
x = 0/2
x = 0

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

Answer 2

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

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

We will eliminate the variable x. To do this, we will multiply the first equation by -5 and the second equation by 2 to make the coefficients of x equal:

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

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

Now, we can add the two equations together to eliminate x:

(-10x - 30y) + (10x - 10y) = 60 + 20
-40y = 80

To solve for y, we divide both sides of the equation by -40:

-40y/(-40) = 80/(-40)
y = -2

Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

2x + 6(-2) = -12
2x - 12 = -12

To solve for x, we add 12 to both sides of the equation:

2x - 12 + 12 = -12 + 12
2x = 0

Dividing both sides of the equation by 2, we find:

x = 0

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