Solve the following system of equations using the elimination method 3x - 4y = -4, x + 3y equals -10 is it -16, 2 and have 16, -2 -4, -2 or -2, -4

Answer 1

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

Let's multiply the second equation by 3, so that the x terms in both equations have the same coefficient:
3(x + 3y) = 3(-10)
3x + 9y = -30

Now we can add the two equations to eliminate the x variable:
(3x - 4y) + (3x + 9y) = -4 + (-30)
6x + 5y = -34

So the system of equations becomes:
6x + 5y = -34
3x - 4y = -4

Now we can solve this system of equations. We can eliminate the x variable by multiplying the second equation by 2 and adding it to the first equation:
(6x + 5y) + 2(3x - 4y) = -34 + 2(-4)
6x + 5y + 6x - 8y = -34 - 8
12x - 3y = -42

We can solve this equation for x:
12x = 3y - 42
x = (3y - 42)/12
x = (y - 14)/4

Now, we can substitute the value of x in terms of y into the first equation:
6((y - 14)/4) + 5y = -34
(3/2)(y - 14) + 5y = -34
(3y - 42)/2 + 5y = -34
3y - 42 + 10y = -68
13y = -26
y = -2

If y = -2, we can substitute this value back into the equation x = (y - 14)/4:
x = (-2 - 14)/4
x = -16/4
x = -4

Therefore, the solution to the system of equations is x = -4 and y = -2.

So the answer is -2, -4.