Find the Mistake
x + y = 24 is the same as y = x + 24
mistake: should be y = -x +24
the form of your answer
(for example is it a line, a number...?)
what is a point (x,y)
what is putting the equation in y= form
the first step of this solving method
what is multiplying by a coefficient?
If given the lines
y = 4x + 3 and y = -3x + 2
multiply to find the equation of a quadratic.
What is y = -12x^2 - x + 6
when multiplying factors to get a quadratic, Mark got
y= (4x -2)(x+7)
y= 4x^2 + 28x + 2x +14
Should have put
y= 4x^2 +28x -2x -14 then
y= 4x^2 +26x -14
the tools that help you solve a system by graphing
What is DESMOS? or What is a graphing calculator?
y = 5
y= 2x +1
(2, 5)
−6x + 6y = 6
−6x + 3y = −12
(5, 6)
Write the quadratic in general (standard form)
y = (x-2)(x+1)
y= x^2 - x -2
4x + 8y = 20
−4x + 2y = −30
solving by elimination, the new equation they found was 6y = -10
should be adding the equations in this case so the x's cancel. Should be 10y = -10
y = x - 11
y = -2x + 19
what is (10, −1)
true or false. You are done once you have found what y equals.
What is false. You need a point meaning x AND y
Name two different coefficients you could multiply the second equation by
−4x − 15y = −17
−x + 5y = −13
What is -4? and What is 3?
Factor the quadratic
y = x^2 + 7x – 8
y = (x -1)(x+8)
to solve y = 4x +9 and 3y+2x = 18 by substitution, the person's first step was:
3y + 2(4x+9) = 18
mistake: the person substituted for x when they should have substituted for y. it should be:
3(4x+9) + 2x = 18.
5x + y = 9
10x − 7y = −18
What is (1, 4)
Write the two equations you would use to solve.
For a choral performance, On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
What is
3x + y = 38
3x + 2y = 52
−7x + y = −19
−2x + 3y = −19
(2, −5)
Find the vertex of the quadratic:
y = 3x^2 + 12x + 9
(-2 , -3)
When finding the vertex of y= (x-4)(x-8) algebraically, the student graphed and found the point (6 , -4) is the lowest point so it must be the vertex.
Directions!! The student solved by graphing not algebraically, they needed to factor the equation, then use the formula -b/2a to find the x value of the vertex. The use the x to find y by substituting into the equation
Solve by graphing
The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. How many students can a van carry? How many students can a bus carry?
What is
Van : 18 students
Bus: 52 students
−4x + 9y = 9
x − 3y = −6
what is (9, 5) ?
5x + 4y = −30
3x − 9y = −18
(−6, 0)
Find the line of symmetry for the quadratic:
y = 2x^2 – 8x – 10
x = 2