Question

l1: solving systems of linear equations
kayla is on level 12 of a new game. every day she completes 6 new levels.
day (x) level (y)
0 12
1 18
2
3
4
5
equation:
$y = mx + b$
maddy is on level 28 of the same game. every day she completes 2 new levels.
day (x) level (y)
0 28
1 30
2
3
4
5
equation:
$y = mx + b$
(graph with day on x - axis and level on y - axis, from 0 to 12 on x and 0 to 50 on y)
when will they be on the same level?
what level will that be?
solution: ( , ) point of intersection
x y

Explanation:

Step1: Find Kayla's equation

Kayla starts at level 12 (when \( x = 0 \), \( y = 12 \)), so \( b = 12 \). She completes 6 levels per day, so slope \( m = 6 \). Her equation is \( y = 6x + 12 \).

Step2: Find Maddy's equation

Maddy starts at level 28 (when \( x = 0 \), \( y = 28 \)), so \( b = 28 \). She completes 2 levels per day, so slope \( m = 2 \). Her equation is \( y = 2x + 28 \).

Step3: Solve the system of equations

Set \( 6x + 12 = 2x + 28 \).
Subtract \( 2x \) from both sides: \( 4x + 12 = 28 \).
Subtract 12 from both sides: \( 4x = 16 \).
Divide by 4: \( x = 4 \).
Substitute \( x = 4 \) into Kayla's equation: \( y = 6(4) + 12 = 24 + 12 = 36 \).

Answer:

(4, 36)