Solutions To Systems
What is a solution to a system of equations?
A solution to a system of equations is an ordered pair (x, y) that is a solution to BOTH equations in the system.
How do you write a system of equations?
We write the two equations inside the curly bracket.
What does it mean for two (or more) equations to be equivalent?
Two (or more) equations are equivalent if they have the same solution(s).
What is the slope of y = -4.2x + 8
-4.2
What does PEMDAS stand for?
Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction
Is (2, 1) a solution to the system
x + y = 3
y = 5x - 9
Yes.
The length of a rectangle is equal to triple the width. Let l be the length and w be the width. Write an equation describing the situation.
l = 3w
True or False:
x + 2 = 7 and x - 5 = 0 are equivalent equations.
True
What does the graph of a linear function look like?
A straight line.
The irrational number 3.1415.... is known as...?
Pi
Is (-5, -3) a solution to the system
x + y = -8
2x - 4y = -2
No.
The knitting club sold 40 scarves and hats at a winter festival and made $700 from the sales. They charged $18 for each scarf and $14 for each hat.
If x represents the number of scarves sold and y represents the number of hats sold, Write a system of equations that represents the constraints in this situation.
x + y = 40
18x + 14y = 700
What does it mean for a number to be a solution to an equation?
A number is a solution to an equation when you plug that number into the equation it makes the equation true
True or false
The y-intercept of 3x - 4y = 12 is -3.
True.
We cannot simplify 100x + 37y because...?
They are not like terms.
Can a systems of TWO linear equations have two solutions? Explain your answer.
No, because two lines only intersect at one point.
At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk?
t + m = 2.10
2t + 3m = 5.15
Create an equation that is equivalent to: 2x + 4 = 19
Answers may vary
Find a solution of the equation
y = -x - 3
Answers vary.
A point on a graph is written in the form (x, y). What is this notation called?
An ordered pair.
The cost of admission to a music concert was $162 for 12 children and 33 adults. The admission was $122 for 88 children and 33 adults in another music concert. Let x be the admission cost for each child, and let y be the admission cost for each adult. How much was the admission for each child and adult?
The cost of admission for each child is $10 and each adult is $14.
The Frosty Ice-Cream Shop sells sundaes for $2 and banana splits for $3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made $156.
Write the system of equations that would allow us to find the amount of sundaes and the amount of banana splits sold on that hot day.
2x + 3y = 156
Where x is the number of Sundaes sold and y in the number of banana splits sold.
Explain why an x value that makes Equation 1 true does not make Equation 2 true.
Equation 1: 2x + 4y = 12
Equation 2: x + 4y = 3
Because the two equations are not equivalent (therefore, they don't have the same solutions).
Find two ordered pairs (x, y) to graph the equation
y = -5x
Amaris says that this system of equations has infinite solutions.
10y - 12 = 20x
5y - 6 = 10x
Is Amaris correct? Explain your answer.
Yes, because the two equations are equivalent.
(i.e. all solutions to the first equations are also solutions to the second equations).