Download Math 006: Systems of Linear Equations 1. Solve y = 5 − 2x x + 2y = 4

Math 006: Systems of Linear Equations
1. Solve
y = 5 − 2x
x + 2y = 4
by graphing.
2. (a) What type of linear system has equations whose graphs are two parallel but nonintersecting lines?
(b) What type of linear system has equations whose graphs are two parallel lines that intersect?
(c) What type of linear system has equations whose graphs are two nonparallel lines?
3. Solve
x − 3y = 3
2x − 6y = 12
4. Solve
7x − y = 4
5x + 2y = 1
5. Solve
4x − 8y = 36
3x − 6y = 27
6. Solve
4x − 2y = 5
2x + 3y = 4
by substitution.
by substitution.
using the addition method.
using the addition method.
7. A rowing team rowing with the current traveled 40 km in 2 h. Against the current, the
teacm could only travel 16 km in 2 h. Find the team’s rowing rate in calm water and the rate
of the current.
Further Practice Related to Khan Academy Videos
8. Solve the system
y = 3x + 1
by graphing
2y + 4 = 6x
9. Solve the following systems of equations using the addition method:
(a)
9x − 4y = −78
4x + y = −18
(b)
−7x − 4y = 9
x + 2y = 3
(c)
−3x − 9y =
66
−7x + 4y = −71
(d)
3t + 5d = 62.5
3t + 2d =
52
(e)
3t + 4g = 6
−6t + g = 6
(f)
2x − y =
14
−6x + 3y = −42
(g) The sum of two numbers is 70. Their difference is 24. What are the two numbers?
(h)
4x − 2y =
5
2x − y = 2.5
(check your solution to (h) by graphing)
10. Solve the following systems of equations by substitution:
(a)
2y = x + 7
x = y − 4
(b)
y = −5x + 8
10x + 2y = −2
(c)
y = − 41 x + 100
y = − 14 x + 120
(d)
y = 4x − 17.5
y + 2x = 6.5
(e)
9x + 3y = 15
y − x = 5
Check your answer to (e) by graphing.
(f) A coin bank contains total of 16 coins consisting of nickels and quarters. The total value of
coins in the bank is $2.00. Find how many nickels and how many quarters are in the bank. Do
this by creating and solving a linear system where n is the number nickels and q is the number
of quarters.
Some further examples from Khan Academy on solving systems of equations by graphing
can be seen in the videos:
Algebra I: Solving systems by graphing and Algebra I: Solving systems by graphing 2