Solve the system by the addition method. $$ \begin{array}{r}x+4 y=-13 \ 4 x+5 y=-19\end{array} $$

Question

UpStudy AI · Accepted Answer

Multiply the first equation by $$4$$ to eliminate $$x$$:

$$
4(x + 4y) = 4(-13) \quad \Rightarrow \quad 4x + 16y = -52
$$

Now subtract the second equation from the result:

$$
(4x + 16y) - (4x + 5y) = -52 - (-19)
$$

Simplify the left side:

$$
4x + 16y - 4x - 5y = 11y
$$

Simplify the right side:

$$
-52 + 19 = -33
$$

Thus, we have:

$$
11y = -33
$$

Solve for $$y$$:

$$
y = \frac{-33}{11} = -3 
$$

Now substitute $$y = -3$$ into the first equation:

$$
x + 4(-3) = -13
$$

Simplify:

$$
x - 12 = -13
$$

Solve for $$x$$:

$$
x = -13 + 12 = -1
$$

The solution to the system is:

$$
x = -1 \quad \text{and} \quad y = -3
$$
The solution is $$ x = -1 $$ and $$ y = -3 $$.

Solve the system by the addition method.