Question

1. -10x - 8y = -12

x + 16y = -14

1. 20x + 4y = 12

-10x + y = 3

Explanation:

Problem 5: Solve the system \(

$$\begin{cases}-10x - 8y=-12\\x + 16y=-14\end{cases}$$

\)

Step 1: Solve the second equation for \(x\)

From \(x + 16y=-14\), we get \(x=-14 - 16y\).

Step 2: Substitute \(x\) into the first equation

Substitute \(x = - 14-16y\) into \(-10x - 8y=-12\):

$$
LATEXBLOCK0
$$

Step 3: Solve for \(y\)

Subtract 140 from both sides:

$$
LATEXBLOCK1
$$

Step 4: Substitute \(y = - 1\) back into \(x=-14 - 16y\)

$$
LATEXBLOCK2
$$

Step 1: Solve the second equation for \(y\)

From \(-10x + y=3\), we get \(y = 10x+3\).

Step 2: Substitute \(y\) into the first equation

Substitute \(y = 10x + 3\) into \(20x + 4y=12\):

$$
LATEXBLOCK0
$$

Step 3: Solve for \(x\)

Subtract 12 from both sides:

$$
LATEXBLOCK1
$$

Step 4: Substitute \(x = 0\) back into \(y = 10x+3\)

$$
LATEXBLOCK2
$$

Answer:

\(x = 2,y=-1\)

Problem 7: Solve the system \(

$$\begin{cases}20x + 4y=12\\-10x + y=3\end{cases}$$

\)