Verbal Answers
Solving Systems
P.T.
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99
Two lines can be the same line, intersect, or be ____________ .
Parallel
99
Solve the system of linear equations by substitution:
y = x - 4
y - 4x = - 10
x - 4 - 4x = - 10
Combine Like Terms
-3x -4 = - 10
Add 4 on both sides
-3x = -6
Divide -3 on both sides
x = 2, then plug in and solve for y
y= 2 - 4
(2,-2)
99
Explain why
x^2+5^2 "does not" = 100^2
Because it's not a right triangle
99
For the first time ever, who was the unanimous winner of the NBA Defensive Player of the Year award?
Victor Wembanyama
99
What is the smallest planet in our solar system (not counting our dwarf planet Pluto)?
Mercury
180
In the Pythagorean theorem (a2 + b2 = c2) what is the special name we give for side c?
The hypotenuse
a & b are called the legs
180
Solve the system of linear equations by elimination:
x + 3y = 5
-x - y = -3
We already have opposites...ready to add...the x will be eliminated
2y = 2
y=1
Plug in y and solve for x.
x + 3 = 5
(2,1)
180
180
Who is our new Head of School?
Dr. Chapman
180
Who is the current US Secretary of State (hint: Florida is his home State as he used to be one of our Senators)
Marco Rubio
360
Solve the system of the linear equations graphed below-
(2,4)
360
Solve the system of linear equations by substitution:
y = 2x + 5
y - 3x = - 1
Substitute 2x + 5 for y in the 2nd equation
2x + 5 - 3x = - 1
Combie 2x - 3x
-x + 5 = -1
Subtract 5 on both sides
-x = -6, thus x = 6
Plug in 6 for x and solve for y = 2(6) + 5
(6,17)
360
Solve for x
x^2+12^2=13^2
x^2+144=169
Subtract 144 on both sides
x^2=25
Take the square root on both sides
x=5
360
This singer won the 2026 Grammy Award for Song of the Year for her track "Wildflower"
Billie Eilish
360
Who won the Responsibility Award?
Harrison
500
Is it possible for a system of linear equations to have exactly two solutions? Explain your reasoning.
No, two lines cannot intersect in exactly two points.
500
Solve the system of linear equations by elimination:
2x + 7y = 1
2x - 4y = 12
Force opposites with the "2x"s by multiplying one of the equations by -1
-2x - 7y = -1
2x - 4y = 12 Then add to cancel x
-11y = 11
y = -1
2x +7(-1) = 1
2x - 7 = 1
x = 4
500
Solve for x
x^2+4^2=5^2
x^2+16=25
Subtract 16 on both sides
x^2=9
Take the square root on both sides
x=3
500
Which live-action popular Disney Movie comes out this summer?
Moana
500
Which Senior is going to the University of Florida next year?
Cam Smith
1000
Describe and correct the error in solving the system of linear equations.
y = -2x + 4
y = -2x + 6
The lines have the same slope so there are infinitely many solutions.
The lines have the same slope but different y-intercepts so therefore they are never going to intersect = No Solution.
1000
Two adult tickets and three kid tickets to the movies cost $66. Four adult tickets and four kid tickets cost $108. How much are adult tickets?
2a + 3k = 66 (multiply both sides by -2)
4a + 4k = 108
-4a - 6k = -132 (this is the top equation after you multiply -2)
Add
-2k = -24
k=12
2a + 3(12) = 66
2a + 36 = 66
2a = 30
a = $15
1000
A 26-foot ladder is leaning against a wall. If the bottom of the ladder is 10 feet from the base of the wall, how high up the wall does the top of the ladder reach?
h^2+10^2=26^2
h^2+100=676
subtract 100 on both sides
h^2=576
Take the square root on both sides
h = 24 feet