Substitution
x = -1
-2x + y = 3
x = -1
y = -12
solution = (-1,-12)
5x - 5y = -40
7x + 5y = 16
x = -2
y = 6
Solution: (-2,6)
y = 2/3x - 1
y = -x + 4
x = 3
y = 1
Solution: (3,1)
Find the value of two numbers if their sum is 12 and their difference is 4.
x + y = 12
x - y = 4
x = 4
y = 8
4x - 12y = 8
-4x + 12y = -6
No Solution
2x - 3y = 50
x = 7
x = 7
y = -12
Solution = (7,-12)
2x - y = -7
2x + 3y = 5
x = -2
y = 3
solution: (-2,3)
4x + y = 2
x - y = 3
x = 1
y = -2
Solution: (1,-2)
The difference of two numbers is 3. Their sum is 13. Find the numbers.
x - y = 3
x + y = 13
x = 8
y = 5
y - 2x = -4
6x - 3y = 12
Infinite
y = 4x - 6
5x + 3y = -1
x = 1
y = -2
Solution = (1,-2)
x + y = -3
5x -2y = -50
x = -8
y = 5
Solution: (-8,5)
2x + y = 2
x = 3
x = 3
y = -4
Solution: (3,-4)
Twice a number minus a second number equals 5. The sum of the two numbers is 16. Find the two numbers.
2x - y = 5
x + y = 16
x = 7
y = 9
Ms Johnson decides to give a test worth 90 points and contains 25 questions. Multiple choice questions are worth three points and word problems are worth four points. How many of each type of question are there?
10 multiple choice
15 word problem
x = -5y - 8
6x + 3y = 6
x = 2
y = -2
Solution = (2,-2)
-2x - 3y = -9
10x + 6y = -18
x = -6
y = 7
Solution: (-6,7)
y = -3
y = 2x +1
x = -2
y = -3
Solution: (-2,-3)
Ben and Sarah bough some pens and pencils. Ben bought 4 pens and 5 pencils for $6.71. Sarah bought 5 pens and 3 pencils for $7.12. Find the cost of each.
Pens cost $1.19
Pencils cost $0.39
x + 5y = 4
3x + 15y = -1
No solution
y - 4x = -1
y - 2x = -5
x = -2
y = -9
Solution: (-2,-9)
3x + 8y = -5
-2x + 2y = 18
x = -7
y = 2
Solution: (-7,2)
y = x - 1
y = -1/4x + 4
x = 4
y = 3
Solution: (4,3)
A collection of nickels and dimes is worth $3.30. If there are 42 coins in all, how many of each kind of coin are there?
24 dimes
18 nickels
y + 2x = 18
6x + 3y = 54
Infinite