Question

cool down: u2l16 - writing and graphing systems of linear equations
solve the system of equations graphically
y + 3 = 2x and y = x + 1
check your solution
success criteria: checkmark all that apply.
i can...
□ i can rewrite each equation in y = mx + b form.
□ i can graph the system of equations with the calculator, label the point of intersection, and verify that the ordered pair satisfies both equations.

Explanation:

Step1: Rewrite first equation

Rewrite \( y + 3 = 2x \) in \( y = mx + b \) form: \( y = 2x - 3 \).

Step2: Identify slopes and intercepts

For \( y = 2x - 3 \), slope \( m = 2 \), y - intercept \( b = - 3 \). For \( y = x + 1 \), slope \( m = 1 \), y - intercept \( b = 1 \).

Step3: Graph the lines

• For \( y = 2x - 3 \): Plot the y - intercept \( (0, - 3) \). Use slope \( 2 \) (rise 2, run 1) to find another point, e.g., \( (1, - 1) \).
• For \( y = x + 1 \): Plot the y - intercept \( (0, 1) \). Use slope \( 1 \) (rise 1, run 1) to find another point, e.g., \( (1, 2) \).

Step4: Find intersection

The lines intersect at \( (4, 5) \).

Step5: Verify the solution

• Substitute \( x = 4 \), \( y = 5 \) into \( y + 3 = 2x \): \( 5 + 3 = 2(4) \) → \( 8 = 8 \) (true).
• Substitute \( x = 4 \), \( y = 5 \) into \( y = x + 1 \): \( 5 = 4 + 1 \) → \( 5 = 5 \) (true).

Answer:

The solution to the system is \( (4, 5) \)