Question

worksheet
solving systems of equations by graphing
name
date
solve each system by graphing (find the point of intersection of the two lines) .

1. $y = 2x - 3$

$y = -3x + 2$

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

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

1. $y = -x + 1$

$x = 3$

1. $y = 4x + 1$

$y = x - 2$

Explanation:

Problem 1: Solve \(

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

\) by Graphing

Step 1: Find Intersection (Algebraically, for Verification)

Set the two equations equal: \( 2x - 3 = -3x + 2 \)
Add \( 3x \) to both sides: \( 5x - 3 = 2 \)
Add \( 3 \) to both sides: \( 5x = 5 \)
Divide by \( 5 \): \( x = 1 \)

Step 2: Substitute \( x = 1 \) into \( y = 2x - 3 \)

\( y = 2(1) - 3 = -1 \)

Problem 2: Solve \(

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

\) by Graphing

Step 1: Find Intersection (Algebraically)

Set \( -\frac{5}{3}x + 1 = -\frac{1}{3}x - 3 \)
Add \( \frac{5}{3}x \) to both sides: \( 1 = \frac{4}{3}x - 3 \)
Add \( 3 \) to both sides: \( 4 = \frac{4}{3}x \)
Multiply by \( \frac{3}{4} \): \( x = 3 \)

Step 2: Substitute \( x = 3 \) into \( y = -\frac{5}{3}x + 1 \)

\( y = -\frac{5}{3}(3) + 1 = -5 + 1 = -4 \)

Problem 3: Solve \(

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

\) by Graphing

Step 1: Substitute \( x = 3 \) into \( y = -x + 1 \)

\( y = -3 + 1 = -2 \)

Problem 4: Solve \(

$$\begin{cases} y = 4x + 1 \\ y = x - 2 \end{cases}$$

\) by Graphing

Answer:

s:

1. Intersection: \( \boldsymbol{(1, -1)} \)
2. Intersection: \( \boldsymbol{(3, -4)} \)
3. Intersection: \( \boldsymbol{(3, -2)} \)
4. Intersection: \( \boldsymbol{(-1, -3)} \)