Question

1. solve the system of equations graphed on the coordinate axes below

$y = -\frac{1}{3}x + 5$
$y = 3x + 5$

1. solve the system of equations graphed on the coordinate axes below.

$y = -\frac{3}{2}x + 4$
$y = 5x + 4$

Explanation:

Problem 1: Solve the system \( y = -\frac{1}{3}x + 5 \) and \( y = 3x + 5 \)

Step 1: Set the equations equal

Since both equal \( y \), set \( -\frac{1}{3}x + 5 = 3x + 5 \).

Step 2: Subtract 5 from both sides

\( -\frac{1}{3}x = 3x \).

Step 3: Add \( \frac{1}{3}x \) to both sides

\( 0 = 3x + \frac{1}{3}x \).

Step 4: Combine like terms

\( 0 = \frac{10}{3}x \).

Step 5: Solve for \( x \)

\( x = 0 \).

Step 6: Substitute \( x = 0 \) into \( y = 3x + 5 \)

\( y = 3(0) + 5 = 5 \).

Step 1: Set the equations equal

\( -\frac{3}{2}x + 4 = 5x + 4 \).

Step 2: Subtract 4 from both sides

\( -\frac{3}{2}x = 5x \).

Step 3: Add \( \frac{3}{2}x \) to both sides

\( 0 = 5x + \frac{3}{2}x \).

Step 4: Combine like terms

\( 0 = \frac{13}{2}x \).

Step 5: Solve for \( x \)

\( x = 0 \).

Step 6: Substitute \( x = 0 \) into \( y = 5x + 4 \)

\( y = 5(0) + 4 = 4 \).

Answer:

The solution is \( (0, 5) \).

Problem 2: Solve the system \( y = -\frac{3}{2}x + 4 \) and \( y = 5x + 4 \)