Question

1.
y = x - 4
y = 4x - 10
2.
y = 2x + 5
y = 3x - 1

Explanation:

It seems these are systems of linear equations to solve (finding the intersection point, I assume). Let's solve each system:

Problem 1: Solve the system \(

$$\begin{cases} y = x - 4 \\ y = 4x - 10 \end{cases}$$

\)

Step 1: Set the two equations equal

Since both equal \( y \), we set \( x - 4 = 4x - 10 \)

Step 2: Solve for \( x \)

Subtract \( x \) from both sides: \( -4 = 3x - 10 \)
Add 10 to both sides: \( 6 = 3x \)
Divide by 3: \( x = 2 \)

Step 3: Find \( y \)

Substitute \( x = 2 \) into \( y = x - 4 \): \( y = 2 - 4 = -2 \)

Step 1: Set the two equations equal

Since both equal \( y \), we set \( 2x + 5 = 3x - 1 \)

Step 2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 5 = x - 1 \)
Add 1 to both sides: \( x = 6 \)

Step 3: Find \( y \)

Substitute \( x = 6 \) into \( y = 2x + 5 \): \( y = 2(6) + 5 = 12 + 5 = 17 \)

Answer:

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

Problem 2: Solve the system \(

$$\begin{cases} y = 2x + 5 \\ y = 3x - 1 \end{cases}$$

\)