The relationships between x, the number of weeks, and y, the number of miles Zara and Steven bike each week, are graphed on the coordinate plane below. What is the point of intersection?
Zara
Steven
0
1
2
3
4
5
6
7
8
9
10
0
20
40
60
80
100
120
140
160
180
200
Time (weeks)
Number of miles
The point of intersection is (
,
).
Great job!
Now that you have found the point of intersection, (3, 120), let’s check that work algebraically. The equations for the relationship between weeks and miles for Zara and Steven are shown below. Since the number of miles Zara bikes will be equal to the number of miles Steven bikes at the solution to this system, you can set the expression for the number of miles they each bike, 60+20x and 90+10x, equal to one another. Do that now.
Zara
Steven
0
1
2
3
4
5
6
7
8
9
10
0
20
40
60
80
100
120
140
160
180
200
Time (weeks)
Number of miles
60+20x
=
90+10x
Good work!
Let’s solve the equation for x, the number of weeks when Zara and Steven bike the same number of miles, to confirm that it’s the same as the x-coordinate of the point of intersection. Since there are x terms on both sides of the equation, let’s get rid of the x term from one of the sides. What move can you make to get rid of the x term on the right side of the equation, 10x, while keeping the equation balanced?
Zara’s miles = Steven's miles
60+20x = 90+10x
Subtract 10x from each side
Multiply each side by 10x
Add 10x to each side
1 answer
To eliminate the \(10x\) on the right side of the equation while maintaining balance, you should:
Subtract \(10x\) from each side.
This will allow you to isolate the \(x\) terms on one side of the equation.
So the equation would be transformed as follows:
\[ 60 + 20x - 10x = 90 + 10x - 10x \]
And this simplifies to:
\[ 60 + 10x = 90 \]
Now you can continue solving for \(x\). Would you like to proceed with the solution from here?
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