Question

understand systems of linear equations - instruction - level
are learning to rock climb. rumi starts at the bottom and climb
starts 10 feet up and climbs 8 feet each minute.
find rumi and noam’s height after
5 minutes.
rumi: 50 feet noam: 50 feet
where do the lines intersect?
the lines intersect at the
point ( , 7 )
noam: y = 8x + 10
rumi: y = 10x
height above ground
number of minutes

Explanation:

Step1: Set up the equations

We have two linear equations: \( y = 10x \) (Rumi's height) and \( y = 8x + 10 \) (Noam's height). To find the intersection, we set them equal: \( 10x = 8x + 10 \).

Step2: Solve for \( x \)

Subtract \( 8x \) from both sides: \( 10x - 8x = 8x + 10 - 8x \), which simplifies to \( 2x = 10 \). Then divide both sides by 2: \( x = \frac{10}{2} = 5 \).

Step3: Find \( y \)

Substitute \( x = 5 \) into \( y = 10x \): \( y = 10 \times 5 = 50 \).

Answer:

\((5, 50)\)