Equivalent Equations
Which of these is equivalent to 2x + 5 = 11?
A. x + 5 = 11
B. 4x = 12
C. 2x = 16
B
A gym charges $20/month + $3/visit. Write equation for total cost in a month C with v visits.
C=20+3v
y = x + 1 and y = 3. State the intersection
(2,3)
Solve: 3x - 4 = 11
x=5
What happens if you add 3 to both sides of an equation?
The equation is equivalent; the solutions are still the same
Select all equivalent to 3(x-2)=9:
A. x-2=3
B. 3x=15
C. x=7
A,B
Movie tickets: $10 adults, $7 kids. Budget $150. Equation?
10a+7k=150
{y=2x, y=x+3}. Solution?
(3,6)
{2x+y=5, x-y=1}
(2,1)
Does multiplying both sides by 2 preserve solutions?
Yes, It creates an equivalent equation; scales both sides evenly
Is 4x-8=12 equivalent to (x-2)=3? Explain.
Yes, divide by 4
Car rental: $50 + $0.30 per mile. Total for 200 miles?
$110
Solve {y+x=4, y-2x=-1}
(5/3,7/3)
Elimination: {3x+2y=7, x-2y=3}
(5/2, -1/4)
Do 4x+2y=10 and 2x+y=5 have the same solutions?
Yes, they are equivalent equations
Which is an equivalent equation to 4-(3x+24)
A) x-20
B) -3x-20
C) 28-3x
B
A Flight costs $200, with a fee of $40 per bag. What is the equation? How much do 5 bags cost?
f=200+40b
400
Graph {y=1/2 x -1, 2y+x=5}. Label solution.
(2,1.5)
Substitution: {y=3x-2, 2x+y=7}
(9/15,17/15)
Explain why adding {x+y=5, 2x-y=1} to get 3x=6 is valid
Hangar diagram; Balance among equations is preserved
(3x+8)/2=5 is equivalent to which equation?
A)3x+8=5
B) x=10
C) (3/2)x=1
C
A pie place sells every pie starting at 5 dollars, with each additional topping costing 2 dollars and each additional filling costing 3 dollars. Create an equation for the situation
p=5+2t+3f
Solution to {x+2y=7, 3x-y=5}
(3/5, -16/5)
2y=x-4, 4x+3y=5
(2,-1)
If we were to treat two equivalent equations like a system of equation, what would happen to the solution set we find?
There will be infinitely many solutions