# Yuri & Kaoru's Weight Loss Journey

### By: Juhi Bora

## The Situation...

Yuri loses 3 pounds each month.

Kaoru loses 7 pounds each month.

*When will Yuri and Kaoru's weight be the same?*

## Yuri's Weight Loss Table

## Equation (Yuri) :

## Kaoru's Weight Loss Table

## Equation (Kaoru) :

## Graph

## Desmos Graphic Solution

**Graphical Solution:**

1. Plot the y-intercept which is (0,180).

2. From that point, use the slope (-3/1 or -3) to graph the line

Kaoru: y=-7x+212

1. Plot the y-intercept which is (0,212).

2. From that point, use the slope (-7/1 or -7) to graph the line

Now you can look at the graph a find the point of intersection/solution, which is (8,156).

**You can also find the solution with the process of substitution-**

Yuri: y=-3x+180

Kaoru: y=-7x+212

If y=y, then that means...-3x+180 = -7x+212

-3x+180 = -7x+212

-3x+7x = 212-180

4x = 32

x = 8

Now we can substitute x into one of the equations to find y

y=-3(8)+180

y=-24+180

y=156

So now you know that x=8 and y=156, therefore the point of intersection is (8,156).

**You can also find the solution with the process of elimination-**

Yuri: y=-3x+180

Kaoru: y=-7x+212

You know that these two equation both have y in common, so we're going to eliminate by making one of the equation negative and subtracting in from the other. This way the positive and negative y, will cancel out.

y= -3x +180

-(y= -7x +212)

0= 4x - 32

32 = 4x

32/4 = x

x=8

Now that we know what x is, we can substitute x in one of the equation to find y.

y= -3(8) +180

y= -24 + 180

y= 156

Therefore the point of intersection/solution is (8,156).