Solve For Y
If y - 5 = x and x = 2, what does y equal?
y = 7
If y = 7 and x + y = 12, what does x equal?
x = 5
For the system of equations y = 3 and x = 5, what point will the 2 lines intersect in?
(5,3)
Armaan works at a nearby pizzeria. It sells pizza for $8 and sandwiches for $6. One day, Armaan notices the sales. The pizzeria sold 8 more pizzas than sandwiches. They made $126 that day. How many pizzas and sandwiches did the store sell?
12 pizzas and 5 sandwiches
Define substitution.
Substitution is a strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable.
If x = y + 3 and x - 2y = 10, what does y equal?
y = 1/2x - 5
If y = 2 and 2x - 4y = 4, what does x equal?
x = 6
For the system of equations 10y = 20x + 40 and 20x - 10y = -40, find the point in which the lines intersect.
all real numbers (every single point on the line since they are the same line)
A number equals 3 times another number minus 2. 5 times the second number plus 2 times the first number is 4. When will these 2 linear equations intersect?
(8/11,2/11)
True or False - The equations can be in any form to use substitution.
False - One equation must say what the variable equals in order to solve (e.g. y = -3x + 7).
If x = 5 and the equation x + 4y = 14, what does y equal?
y = 9/4
If y = -4x + 11 and -2x - 5y = 17, what does x equal?
x = 4
DOUBLE JEOPARDY! - Challenge question. If x – 6y – 2z = -8, -x + 5y + 3z = 2, and 3x – 2y – 4z = 18, what is the coordinate in which these points will intersect?
Hint: (x, y, z) - When you reach your answer, think of the coordinate as a cube for the grid - not a square!
This question gives you/takes away as many points as you wager.
(4,3,-3)
Neha begins to race Kaushik in a 1 mile race. Kaushik cheats and gets a 1/2 mile head start. He runs at a pace of 1/20 miles per minute. Meanwhile, Neha runs at a pace of 1/10 miles per minute at the beginning. Using substitution, figure out who will win the mile race.
What is a system of equations?
A system of equations is a collection of two or more linear equations with the same variables.
If x - 5(y + 3x) = 10 and 10x + 5y = 20, what does x equal?
y = 19
If y = -3x - 7 and 6x + 2y = -15, what does x equal?
no solution
For the system of equations 2x - 4y = 92 and y = 5x - 7, what point will they intersect at?
(-32/9,-223/9)
Krish did a study to figure out how many students rode to school in cars and buses (out of the 231 students). He found out that some students rode in buses (which held 25 students each) and cars (in which 7 people carpooled together per car). 15 vehicles were used in total. How many of each vehicle were used?
7 buses and 8 cars
DOUBLE JEOPARDY! - Is it possible to get an answer of no solution/all real numbers for the solution of a system of equations? If so, demonstrate a problem of each.
Yes - answers may vary
If x = 8y - 3(2y) and 5x + 2(3y - 4) = 21, what does y equal?
y = 29/16
If x - y = 5 and -2x + 2y = -10, what does x equal?
all real numbers
If -5x + y = -2 and -3x + 6y = -12, what is the point in which they will intersect at?
(0,-2)
Abhishek wants to get himself a rectangular pool. He wants the most value for the best price. Pool School sells them for $15 per foot of length (l). Meanwhile, Pool Paradise Party sells them for $25 plus $5 per foot of length. Abhishek wants to know what would have the best value for 5 feet of length. In this scenario, which pool would have the best value?
Pool Paradise Party
What is the solution to a system of equations?
The solution is the point in which the lines intersect with one another.