Solve the following system of equations using the elimination method.
3x-4y =- 4, x+3y =- 10
To solve this system of equations using the elimination method, we can assume that the two equations are already in standard form, i.e., in the form ax + by = c.
The given system of equations is:
3x - 4y = -4 ...(1)
x + 3y = -10 ...(2)
To eliminate x, we need to multiply equation (2) by 3 and equation (1) by 1:
(3)(x + 3y) = (3)(-10) <=> 3x + 9y = -30 ...(3)
1(3x - 4y) = 1(-4) <=> 3x - 4y = -4 ...(4)
Now, we subtract equation (4) from equation (3):
(3x + 9y) - (3x - 4y) = (-30) - (-4)
3x + 9y - 3x + 4y = -30 + 4
13y = -26
Dividing both sides of the equation by 13:
13y/13 = -26/13
y = -2
Now that we have the value of y, we can substitute it back into equation (1) to find x:
3x - 4(-2) = -4
3x + 8 = -4
3x = -4 - 8
3x = -12
x = -12/3
x = -4
Therefore, the solution to this system of equations is x = -4 and y = -2.