Substitution Method
Using the substitution method, Vito is solving the following system of equations algebraically:
y + 3x = -4
2x - 3y = -21
Which equivalent equation could Vito use?
1) 2(−3x − 4) + 3x = −21
2) 2(3x − 4) + 3x = −21
3) 2x − 3(−3x − 4) = −21
4) 2x − 3(3x − 4) = −21
What is
Ans: (3)
2x − 3(−3x − 4) = −21
A system of equations is shown below.
Equation A: 5x + 9y = 12
Equation B: 4x − 3y = 8
Which method eliminates one of the variables?
1) Multiply equation A by −1/3 and add the
result to equation B.
2) Multiply equation B by 3 and add the
result to equation A.
3) Multiply equation A by 2 and equation B
by −6 and add the results together.
4) Multiply equation B by 5 and equation A
by 4 and add the results together.
What Is
Ans: (2)
Multiply equation B by 3 and add the
result to equation A.
Aiden runs a farm stand that sells apples and strawberries. Each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a total of 35 pounds of apples and strawberries. Write a system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold. Define the variables and write the system of equation.
What is
Let a = the number of pounds of apples sold
Let s = the number of pounds of strawberries sold
Write System of Equations:
2a + 3s = 80
a + s = 35
What is the Slope-Intercept Formula?
What is
y = mx + b
What is a Linear Equation?
An Linear Equation is
What is the solution to the system of equations below?
-4x - 6y = -48
y = -2x
What is
Ans: (-6, 12)
Which pair of equations could not be used to solve the following equations for x and y?
4x + 2y = 22
-2x + 2y = 12
1) 4x + 2y = 22
2x - 2y = 8
2) 4x + 2y = 22
-4x + 4y = -16
3) 12x + 6y = 66
6x - 6y = 24
4) 8x + 4y = 44
-8x + 8y = -8
What is
Ans: (4)
4) 8x + 4y = 44
-8x + 8y = -8
Parker owns a food truck that sells tacos and burritos. He sells each taco for $4.50 and each burrito for $6.75. Yesterday Parker made a total of $576 in revenue from all burrito and taco sales and there were twice as many burritos sold as there were tacos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables and write the system of equation.
What is
Define Variables:
Let t = the number of tacos sold
Let b = the number of burritos sold
Write System of Equations:
4.50t + 6.75b = 576
b = 2t
What is 12 x 12
What is
144
What is the Slope Formula
What is
m = y2 - y1 / x2 - x1
What is the solution to the system of equations below?
y = 2x + 8
3(-2x + y) = 12
1) No Solution
2) Infinite Solutions
3) (-1,6)
4) (1/2,9)
What is
Ans: (1)
No Solution
What is the solution to the system of equations below?
-2x + 4y = -4
6x + 6y = -24
What is
Ans: (-2,-2)
Josue has $0.33 worth of pennies and nickels. He has a total of 13 pennies and nickels altogether. Write a system of equations that could be used to determine the number of pennies and the number of nickels that Josue has. Define the variables and write the system of equation.
What is
Define Variables:
Let p = the number of pennies
Let n = the number of nickels
Write System of Equations:
0.01p + 0.05 = 0.33
p + n = 13
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
2x + y = 4
4x + 2y = 8
What is
Infinitely Many Solutions
What is b
10b + 18 = 28
What is
b = 1
What is the solution to the system of equations below?
8x +7y = -47
4y - 1 = x
What is
Ans: (-5,-1)
What is the solution to the system of equations below?
6x + 6y = 6
9x + 2y = 16
What is
Ans: (2, -1)
Jayden went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 200 mg of sodium and each frozen dinner has 650 mg of sodium. Jayden purchased a total of 13 cans of soup and frozen dinners which collectively contain 4400 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables and write the system of equation.
What is
Define Variables:
Let c = the number of cans of soup purchased
Let f = the number of frozen dinners purchased
Write System of Equations:
200c + 650f = 4400
c + f = 13
Solve:
5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13
What is
0 = 0
What is x
10x - 1 = 7x + 26
What is
x = 9
What is the solution to the system of equations below?
-3x + 6y = 45
x = 8y + 9
What is
Ans: (-23, -4)
What is the solution to the system of equations below?
-x + 2y = -2
6x - y = -43
What is
Ans: (-8,-5)
A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 12 granola bars and each large box has 18 granola bars. The camp bought a total of 15 boxes that have 240 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables and write the system of equation.
What is
Define Variables:
Let s = the number of small boxes
Let l = the number of large boxes purchased
Write System of Equations:
12s +18l = 240
s + l = 15
If 3x + 4y = 8 is a true equation, what would be the value of 4y + 3x?
What is 4y + 3x = 8
What is the GCF of 21 and 6
What is
GCF: 3