Solving by Substitution
y = 2x − 2
−x + 2y = −4
What is (0, − 2) ?
y = x − 1
y = −x + 3
What is (2, 1) ?
y = 2x + 9
y = 6 − x
What is (−1, 7) ?
The length of a rectangle is 8 feet more than its width. The perimeter of the rectangle is 72 feet. Find the width of the rectangle.
What is 14 ft?
x − y = 5
− 3x + y = − 1
What is (−2, −7) ?
y = −5x + 14
y = x − 10
What is (4, −6) ?
y = −x − 4
y = 3/5 x + 4
What is (−5, 1) ?
You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in 22 minutes. Write a system of linear equations that represents this situation. How long does it take you to jog around the park?
What is: 2x + y = 10 and 2x + 3y = 22; 6 min?
x = 5y + 3
2x + 4y = − 1
What is ( 1/2 , −1/2 ) ?
y = x
y = 2x + 1
What is (−1, −1) ?
y = 2x + 5
y = 1/2 x − 1
What is (−4, −3) ?
You and your friend are selling raffle tickets for a new laptop. You sell 14 more tickets than your friend sells. Together, you and your friend sell 58 tickets. a. Write a system of linear equations that represents this situation. b. How many tickets do each of you sell?
What is you: 36 tickets, your friend: 22 tickets?
y = 2x + 3
y = 5x
What is (1, 5) ?
y = − 4x − 7
x + y = 2
What is (−3, 5) ?
x + y = 27
y = x + 3
What is (12, 15) ?
You have a total of 10 coins consisting of nickels and dimes in your pocket. Th e value of the coins is $0.70. Write and solve a system of linear equations to fi nd the numbers of nickels and dimes in your pocket.
What is 6 nickels, 4 dimes?
4x + 2y = 0
y = 1/2 x − 5
What is (2, −4) ?
x − y = 7
0.5x + y = 5
What is (8, 1) ?
1/2 x + y = − 6
6x + 2y = 8
What is (4, −8) ?
A gift basket that contains jars of jam and packages of bread mix costs $45. Th ere are 8 items in the basket. Jars of jam cost $6 each, and packages of bread mix cost $5 each. Write and solve a system of linear equations to fi nd the number of each item in the gift basket.
What is 5 jars of jam, 3 packages of bread mix?