I am not getting any of the posted answers:
Solve the system using elimination.
2x + 6y = -12 and 5x – 5y =10
(2, 1)
(0, –2)
(–2, 0)
(1, 2)
A quick glance at the equations shows that both can be reduced to simpler form
2x + 6y = -12 ---> x + 3y = -6
5x - 5y = 10 ----> x - y = 2
subtract them:
4y = -8
y = -2
sub into x-y=2
x+2 = 2
x = 0 -------- x=0, y=-2
Hope this is correct
To solve the system of equations using elimination, we can eliminate one variable by multiplying one or both equations by a suitable constant so that the coefficients of one variable in both equations will cancel out when added or subtracted together.
Here are the steps to solve the system using elimination:
1. Multiply the second equation by 2 to make the coefficients of x in both equations equal:
2(5x - 5y) = 2(10)
10x - 10y = 20
2. Now, we have two equations with equal coefficients for x. Add the two equations together to eliminate x:
(2x + 6y) + (10x - 10y) = -12 + 20
12x - 4y = 8
3. Simplify the equation:
12x - 4y = 8
4. Divide the equation by 4 to simplify further:
(12x - 4y)/4 = 8/4
3x - y = 2
5. Now, we have a new equation: 3x - y = 2.
To find the values of x and y, rearrange the equation in terms of one variable:
y = 3x - 2
Now we can substitute this equation into either of the original equations to solve for the other variable. Let's substitute it into the first equation (2x + 6y = -12):
2x + 6(3x - 2) = -12
2x + 18x - 12 = -12
20x - 12 = -12
20x = 0
x = 0
Now substitute the value of x back into the equation y = 3x - 2:
y = 3(0) - 2
y = -2
Therefore, the solution to the system of equations is (x, y) = (0, -2).
So the correct option is (0, –2).
To solve the system using elimination, we want to eliminate one variable by adding or subtracting the two equations. Let's start with the given system of equations:
2x + 6y = -12 (Equation 1)
5x - 5y = 10 (Equation 2)
To eliminate one variable, we need to find a way to make the coefficients in front of either the x or y term the same or opposite in the two equations.
Let's multiply Equation 1 by 5, and Equation 2 by 2 to make the coefficients of x the same:
10x + 30y = -60 (Equation 3) [Multiply Equation 1 by 5]
10x - 10y = 20 (Equation 4) [Multiply Equation 2 by 2]
Now, we can subtract Equation 4 from Equation 3 to eliminate the x term:
(10x + 30y) - (10x - 10y) = -60 - 20
10x + 30y - 10x + 10y = -80
40y = -80
Dividing both sides of the equation by 40, we get:
y = -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 Equation 1:
2x + 6(-2) = -12
2x - 12 = -12
2x = 0
x = 0/2
x = 0
Therefore, the solution to the system of equations is (x, y) = (0, -2).
So, the correct answer is option (0, -2).