Page 181 - Math Course 2 (Book 1)

Systems of Equations

Words You have information about the amount Your Turn!
of time spent riding and walking.
You also know the rates and the total Solve a System of Equations
distance traveled.
Graph the system of equations. Then determine
Variables Let r equal the number of hours they whether the system has no solution, one solution,
rode and w equal the number of hours or inf nitely many solutions. If the system has one
they walked. Write a system of solution, name it.
equations to represent the situation.
y = 2x + 3
1
Equations y = x + 3
2
the total A. one; (0, 3) B. no solution
The the number C. inf nitely many D. one; (3, 3)
number number of hours
of hours of hours of the Answer
riding plus walking equals trip.
y
r + w = 3

The the the total 0
distance distance distance
traveled traveled of the x
riding plus walking equals trip.

12r + 4w = 20

Graph the equations r + w = 3 and 12r + 4w = 20.
Graph the system of equations. Then determine
y
whether the system has no solution, one solution,
12r + 4w = 20 or inf nitely many solutions. If the system has one
solution, name it.
x + 3y = 4
r + w = 3 1
x + y = 0
3
A. one; (0, 0) B. no solution
0 x C. inf nitely many D. one; (1, 3)

Answer
The graphs appear to intersect at the point with the
coordinates (1, 2). Check this estimate by replacing y
r with 1 and w with 2 in each equation.

Check
r + w = 3 12r + 4w = 20

1 + 2 = 3 12(1) + 4(2) = 20 0

3 = 3 12 + 8 = 20 x

Tyler and Pearl walked for 2
Answer
hours.

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