Solve the following system of equations using the elimination method.

3х - 4y =-4, x +3y=-10
(1 point)
О (-16, -2)
O (-1,-2)
O (-2,-4)
O (-16,2)

1 answer

To solve the system of equations using the elimination method, we start with the given equations:

  1. \( 3x - 4y = -4 \)
  2. \( x + 3y = -10 \)

We will eliminate \( x \) or \( y \) by manipulating these equations. In this case, let's eliminate \( x \).

First, we can multiply the second equation by 3 so that the coefficients of \( x \) in both equations become the same:

\[ 3(x + 3y) = 3(-10) \ 3x + 9y = -30 \tag{3} \]

Now we have the modified system:

  1. \( 3x - 4y = -4 \)
  2. \( 3x + 9y = -30 \)

Next, we can eliminate \( x \) by subtracting equation 1 from equation 3:

\[ (3x + 9y) - (3x - 4y) = -30 - (-4) \ 3x + 9y - 3x + 4y = -30 + 4 \ 13y = -26 \]

Now, solve for \( y \):

\[ y = \frac{-26}{13} = -2 \]

Now that we have \( y \), we can substitute this value back into one of the original equations to find \( x \). We'll use the second equation \( x + 3y = -10 \):

\[ x + 3(-2) = -10 \ x - 6 = -10 \ x = -10 + 6 \ x = -4 \]

So the solution to the system of equations is:

\[ (x, y) = (-4, -2) \]

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