Solve Using Any Method
y = 2x - 2
-x + 2y = -4
(0,-2)
y = 2x + 3
y = 5x
(1,5)
x + 3y = -2
x - 3y = 16
(7,-3)
Without graphing or solving, determine the number of solutions to the system. Explain your reasoning.
y = 5x - 9
y = 5x + 9
no solution; the lines are parallel
Your family is buying tickets for an amusement park. Child tickets are $20 each, and adult tickets are $50. Your family buys a total of 10 tickets and spends $320. How many of each ticket you purchase?
4 adult tickets and 6 child tickets
y = x + 1
y = 4x + 7
(-2,-1)
y = 2x - 4
7x - 2y = 5
(-1,-6)
2x - y = 9
4x + y = 21
(5,1)
Without graphing or solving, determine the number of solutions to the system. Explain your reasoning.
y = 6x + 2
y = 3x + 1
1 solution; Different slopes
You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject?
26 math problems
16 science problems
x - y= 5
-3x + y = -1
(-2,-7)
4x + 2y = 0
y = 1/2x -5
(2,-4)
-5x + 2y = 13
5x + y = -1
(-1,4)
Without graphing or solving, determine the number of solutions to the system. Explain your reasoning.
y = 8x - 2
y + 8x = -2
1 solution; different slopes
You are planning a party and buy a total of 50 hamburgers and hotdogs for $90. You pay $2 per hamburger and $1.50 per hotdog. How many of each did you buy?
30 hamburgers and 20 hotdogs
y = -4x - 7
x + y = 2
(-3.5)
x = 5y + 3
2x + 4y = -1
(1/2, - 1/2)
-6x + 5y = 25
-2x - 4y =14
(-5,-1)
Without graphing or solving, determine the number of solutions to the system. Explain your reasoning.
4y - 4x= 8
y = x + 2
infinitely many solutions; same equations
A hospital employs a total of 77 nurses and doctors. The ratio of nurses to doctors is 9:2. How many nurses and doctors are employed at the hospital?
63 nurses 14 doctors
1/2 x + y = -6
-x + 3y = 8
(4,-8)
2x + 3y = -3
2x = y + 5
(1.5, -2)
5y = 15 - 5x
y = -2x + 3
(0,3)
Without graphing or solving, determine the number of solutions to the system. Explain your reasoning.
2x - 4y = 10
-12x + 24y = -60
Infinitely many solutions; same equation
The measure of the obtuse angle in an isosceles triangle is 2.5 times the measure of one of the acute angles. Write and solve a system of linear equations to solve for the measure of each angle in the isosceles triangle.
40,40,100