Math 100A
Systems of Linear Equations I
Name:
1. Determine whether the given ordered pairs are solutions of the system of linear equations
x − 2y = 11
3x + 2y = −1
(a) (−5, 3)
(b) (−3, 4)
2. Solve the systems of linear equations.
(a)
3x + y = 10
x + 2y = 15
(b)
2p + 3r = 10
−5p + 2r = 13
Math 100A
Systems of Linear Equations I
(c)
x + 3y = 0
−2x + 4y = 30
(d)
2p + 5q = 14
5p − 3q = 4
3. Solve the systems of equations, and graph. Make sure to label your solution.
(a)
y = 6x − 7
y = 3x + 2
y
✻
5
✲
−10
−5
5
−5
−10
Page 2
x
Math 100A
Systems of Linear Equations I
(b)
2x + 5y = 7
−3x + 2y = 1
y
✻
5
✲
−10
−5
5
−5
4. For the system
−10
Ax + 3By = 2
−3Ax + By = −11,
find A and B such that x = 3, y = 1 is a solution.
Page 3
x
Math 100A
Systems of Linear Equations I
!
"
5. Write a system of equations that has − 12 , 17
as a solution.
6
6. For the system
2x + 3y = 5
4x + 6y = n,
what must be true about n in order for there to be infinitely many solutions? Explain.
7. Janice is thinking of two numbers. She says that two times the first number plus the second
number is 47. In addition, the first number plus three times the second number is 81. Find the
numbers.
8. Johnny has $6.75 in dimes and quarters. He has 8 more dimes than quarters. How many
quarters does Johnny have? How many dimes does Johnny have?
Page 4