Math 152
Chapter 3 Handout
Helene Payne
Name:
1. Determine whether the given ordered pair is a solution to the system.
(a) (6, 2)
(b) (−3, −3)
x+y =8
x−y =4
x − 2y = 3
2x − y = −9
2. Graph each system of equations and give the solution. If there is no solution or infinitely many solutions, state that.
(a) y = x − 5
y = −2x + 4
(b) x + 2y = 10
1
y =− x+1
2
Math 152
Chapter 3 Handout
3. Solve each system using the method of your choice.
(a)
3x + 2y = 7
y = 3y − 5
(b)
4x − 2y = 10
y = 2x − 5
(c)
x+y =8
x − y = 10
(d)
6x + 2y = 18
3x + y = 10
(e)
5x + 27y = 27
7x − 9y = −9
Page 2
Helene Payne
Math 152
Chapter 3 Handout
Helene Payne
Word Problems
4. One number is four more than twice another. Their sum is 34. Find the
numbers.
5. Melinda is a single mom, working two jobs just to make ends meet. She
makes $11.00 an hour as a receptionist in a dental office and on weekends
she works at a shoe store in the mall making $8.00 an hour. One week
she worked 49 hours and made $506. How many hours did she work at
each job?
6. A chemist must mix a 10% alcohol solution and a 43% alcohol solution
to get 110 milliliters of a 31% solution. How many milliliters of each
solution should be mixed to get the desired solution?
Page 3
Math 152
Chapter 3 Handout
Helene Payne
7. Bonnie invested $8, 000 in two accounts paying 5% and 6% annual interest. Her money earned a total of $445 in interest in one year. How much
was invested in each account?
8. A boat can travel 20 miles downstream in 2 hours, but it takes 3 hours
to travel 18 miles upstream. Find the speed of the boat in still water and
the speed of the current.
9. Determine if the given ordered triple is a solution of the system.
(a) (1, −2, 3)
(b) (−3, −1, 2)
x+y+z =2
x − y + 2z = 9
3x + 2y + z = 2
x + y + z = −2
x − y + 5z = −12
3x + y + z = 2
Page 4
Math 152
Chapter 3 Handout
Helene Payne
10. Solve each system. If there is no solution or if there are infinitely many
solutions and the system’s equations are dependent, state that.
(a)
x+y+z =6
2x − y − 3z = −5
4x + y − 3z = 5
(b)
x − y + 3z = 1
3x + z = 0
− x + y − 3z = −5
Page 5
Math 152
Chapter 3 Handout
(c)
2x + y − 3z = −3
4x + 2y − 6z = −6
3x − 2y + 4z = 1
Page 6
Helene Payne
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