Solve using elimination.
2x + 6y = 6
2x + 3y = 12
Just subtract them they way they are ...
3y = -6
y = -2
now sub that into either equation to find the x
3x + 4y = -14
3x − 10y = 14
do it the same way. Subtract to eliminate x.
To solve this system of equations using elimination, we need to eliminate one of the variables by manipulating the equations. Let's start by multiplying the second equation by -2 to make the coefficients of the x term the same in both equations.
Original equations:
2x + 6y = 6 (equation 1)
2x + 3y = 12 (equation 2)
Multiply equation 2 by -2:
-4x - 6y = -24 (equation 3)
Now, let's add equation 1 and equation 3 together to eliminate the x variable:
(2x + 6y) + (-4x - 6y) = 6 + (-24)
2x - 4x + 6y - 6y = -18
-2x = -18
Simplifying the equation, we get:
-2x = -18
To solve for x, divide both sides of the equation by -2:
x = -18 / -2
x = 9
Now, substitute the value of x back into one of the original equations (let's use equation 1) to solve for y:
2x + 6y = 6
2(9) + 6y = 6
18 + 6y = 6
Now, isolate the y variable by moving the constant term to the other side:
6y = 6 - 18
6y = -12
Finally, solve for y by dividing both sides of the equation by 6:
y = -12 / 6
y = -2
So, the solution to the system of equations is x = 9 and y = -2.