Elimination
{3x+2y=9}
{2x+6y=6}
If you answered (3,0) then you are correct let's see how we got this answer.
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{x-2y=8}
{x+y=5}
If you answered (6,-1) you are correct let's see our solving steps.
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Emma is planning to bake cookies for a bake sale. She needs to buy flour and sugar. The cost of flour is $2.50 per pound, and the cost of sugar is 43.00 per pound. Emma wants to spend a total of $15 on flour and sugar combined. However, there was a mix-up at the store and Emma accidentally switched the prices of flour and sugar on her shopping list.
1. 2.50(4) + 3.00y=15
2. 10+ 3.00y15
3. 3.00y =5
y=5/3
What went wrong: The value of the y is a fraction which doesn't make sense in this content.
y=5x + 10 solve this using linear equations.
If answered correctly you should have y=25 our steps to get this are quick and simple let's have a look.
y= 5(3) +10
Simplify
y=15+10
y=25
Sienna is saving money to buy a new phone. She currently has $50, and each week she saves $10. At the same time, the price of the phone she wants is decreasing by $5 every week. The total cost of the phone is in the equation C = 150 - 5w, C is the cost in dollars and w is the number of weeks.
to find this you should have got that she can buy the phone she wants in about 7 weeks we can find this by following this
1. Equation for Sienna’s savings S:
Sienna saves $10 per week, and she starts with $50. So, the equation is S = 10w + 50, and W is the number of weeks.
2. Equation for the phone cost C:
The cost equation is given as C = 150 - 5w, where w is the number of weeks.
3. Graph the Equations:
Plot both equations on the same set of axes. The point where Sienna’s savings S equals the smartphone cost C is the solution.
4. Find the Solution:
Set S equal to C and solve for w:
10w + 50 = 150 - 5w Simplify and solve for w. Once you find w, you can substitute it back into either S or C to find the amount.
{4x-7y=2}
{3x-3y=6}
If you answered (4,2) then you are correct let's see how we got this answer.
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{y=5x-1}
{2y= 3x+12}
If you answered (2,9) you are correct let's see our solving steps.
2(5x-1) = 3x+12
2(5x-1) = 3x +12
-3x -3x
2. 7x -2 = 12
+2 +2
3. 7x = 14
7x/7 = 14/7
x=2
4. y=5x-1
y=5(2) -1
y=9
x-3=10
To find this mistake we would add 3 to each side of the equation to isolate the x
So the mistake is that I initially stated x was subtracted by 3 instead of adding 3
Amber is saving up to buy a new bike. She currently has $100 saved and plans to save $20 each week from her allowance. Solve using linear equations.
If answered correctly you should have x=10 our steps to get this are quick and simple let's have a look.
Let’s use the equation y=20x+100, where y represents the total amount of money Amber has saved after x weeks.
20x+100=300
Subtract 100 from both sides of the equation to isolate the term with x: 20x=200
Divided both sides of the equations by 20 to solve for x
x=10
If Sarah sells 5 cups of lemonade, she sells each cup for $2 how much will she make in total? Graph this equation
if you did this correctly you would Graph The equation by plotting different values of x and their corresponding values of y.
y= $2(5)
y=$10
Solve this equation using elimination. Sara and John went to a store to buy some toys. Sara bought 3 dolls and 2 cars, and the total cost was $25. John bought 2 dolls and 4 cars, and the total cost was $32. What's your answer? show your work.
the solution is d = 4.5 and c = 5.75.if you got this you are correct if not let's see the steps we took to get here.
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Sarah and Alex are selling cookies for a school fundraiser. Sarah sold twice as many boxes as Alex. Together, they sold a total of 18 boxes of cookies. Solve using substitution
if you did this correctly you would get that Alex sold 6 boxes, and James sold 12 boxes. Heres how
Let's use substitution to represent the number of boxes each person sold. Let A be the number of boxes Alex sold and J be the number of James sold.
Given that James sold twice as many boxes as Alex:
J = 2A
Together, they sold a total of 18 boxes:
J + A = 18
Now, substitute the first equation with the second:
2A + A = 18
Combine like terms:
3A = 18
Divide by 3 to find the number of boxes Alex sold:
A = 6
Now substitute this value back into the first equation to find the number of boxes Sarah sold:
J = 2 x 6 = 12
So, Alex sold 6 boxes, and James sold 12 boxes.
Equation 1: 2x+3y=10
Equation 2: 4x-2y=5
2x= 10-3y
x=(10-3y)2
4(10-3y)2+2y=5
What went wrong: the equation is becoming more complicated when it's not needed.
3x - 5 = 10
If answered correctly you should have x=5 our steps to get this are quick and simple let's have a look.
1. Add 5 to both sides:
3x = 15
2. Divide both sides by 3:
x = 5
So, the solution to the equation is x = 5.
Hannah is saving money for a Drake concert ticket she needs $55. She starts with $30 and saves $5 per week. In how many weeks will she have what she needs? The total amount saved S after w weeks can be represented by the equation S = 5w + 30.
If answerd correctly you should have 5 weeks these are our solving steps.
1. Equation for Hannah's savings S:
The equation is S = 5w + 30, and W is the number of weeks.
2. Graph the Equation:
Plot the equation S = 5w + 30 on a graph.
3. Find the Solution:
Determine the point on the graph where S equals $55. This corresponds to the number of weeks W it takes for Hannah to save $55.
5w + 30 = 55
Solve for w:
5w = 25
w = 5
So, Hannah will have saved $55 in 5 weeks.
Samantha has twice as many apples as oranges. Together, she has 18 pieces of fruit. How many apples and oranges does Samantha have?
Remember to use elimination to solve for the number of apples and oranges.
if you got that Samantha has 12 apples and 6 oranges. let's see our solving steps
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{y= x-1}
{y=2x =2}
If you answered (-3,-4) you are correct let's see our solving steps.
{x-2y=8}
{x+y=5}
1. x-1= 2x -2
-x -x
2. -1 = x+2
-2 -2
3. -3=x
4. y=2x+2
y=2(-3)+2=-4
Solution:(-3,-4)
Sarah is organizing a party and wants to order pizza for her guests. She decides to order large pizzas, which cost $12 each, and small pizzas, which cost $8 each, Sarah wants to spend a total of $80 on pizzas. However, there was a mix-up at the pizza place and got switches on the menu
12(5)+8y=80
60+8y+80
8y=20
y=20/8
y=2.5
What went wrong: the value of y is a decimal which doesn't make sense in this equation.
y=2x-5 solve this using linear equations
If answered correctly you should have y=3 our steps to get this are quick and simple let's have a look.
1.y=2(4)-5
2.Simplify
3.y=8-5
4.y=3
If Alex has 10 gallons of gas, each gallon costs $3.50 what will the total cost be? Graph this equation.
if you did this correctly you would Graph The equation by plotting different values of x and their corresponding values of y.
y=3.50(10)
y=35
{x+y=4}
{2x-3y=18}
If you answered (6,-2) then you are correct let's see how we got this answer.
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Lily and Ben are saving money for a trip. Lily saved $40 more than Ben. Together, they have a total of $180 saved. Solve using substitution
if answered correctly you' d get Ben saved $70, and Lily saved $70 + $40 = $110. Heres how
B + (B + $40) = $180
Combine like terms:
2B + $40 = $180
Subtract $40 from both sides:
2B = $140
Divide by 2:
B = $70
So, Ben saved $70, and Lily saved $70 + $40 = $110.
3z+7+16
This doesn't need to be corrected.
John is planning a road trip and wants to rent a car. The car rental company charges a flat fee of $50 plus $30 per day for the rental. Solve using linear equations.
If answered correctly you should have y=140 our steps to get this are quick and simple let's have a look.
Let's use the equation y= 30x + 50, where y represents the total cost of renting the car for x days
y=30(3)+ 50
y=90+50
y=140
Rankin bikes at a constant speed of 12 miles per hour. The distance he travels D in t hours is shown by the equation D = 12t. Graph the equation to find out how far Rankin will have traveled in 2.5 hours.
If answerd correctly you should have that Rankin will have traveled 30 miles in 2.5 hours. these are our solving steps.
1. Equation for Rankin’s distance D:
The equation is D = 12t, and t is the time in hours.
2. Graph the Equation:
Plot the equation D = 12t on a graph.
3. Find the Solution:
Determine the point on the graph where t equals 2.5 hours. This corresponds to the distance D Rankin will have traveled.
D = 12 x 2.5
Find the answer:
D = 30
So, Rankin will have traveled 30 miles in 2.5 hours.