Question

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)

Answer 1

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

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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