1 The point (5, -3) is a solution to which system of equations?
y=x-8
2x+y=7
2 How many solutions does the system of equations have?
y=−2x+12
4y+x−20=0
one solution***
3
first box -1.5, 4.5
second box no solution
third box 1,1
fourth box (-1,2)
it may be randomize so these may not be correct use at your own risk
4 A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 225 cars and trucks. Dealership B sells twice as many cars and half as many trucks as the Dealership A, and sells a total of 300 cars and trucks.
a)x+y=225
b)2x+1/2y=300
c)125
d)50
5 The sum of two numbers is 22. Three times one number increased by five is 35.
a)x+y=22 and 3x+5=35
b)10 and 12
6 Joelle currently has 18 rocks in her collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week. Set up a system of equations to show how many rocks each has in their collection.
a) 4x+18
b)3x+30
c)12
d)66
7) Which graph represents the solution for the equation −52x−1=4x+2
?
its the one that looks like a X
8)Solve the system of equations using your Desmos calculator:
3x+2y=2
−2x+y=8
(-2,4)***
9 Not including tax, a total of 19 pens and markers cost $11.50. The pens cost $0.25 each, and the markers cost $0.75 each. Write the system of equations that could be used to solve for the number of pens, p, and the number of markers, m, bought.
p+m=19
0.25p+0.75m=11.50
10 Joyce wants to go to the zoo with her friend over spring break. You can pay $45 to get into the zoo each time, or join a membership for $50 and then only pay $20 each visit to the zoo. How many times will Joyce need to visit the zoo to justify the expense of the membership fee?
3***
11 Two systems of equations are shown:
4x+y=−1
x+y=2
and
8x+2y=−2
−4x+cy=−8
What would the value of c need to be to get the same solution for both systems?
-4***
12 Susie determined that the system of equations below has infinitely many solutions.
The first line goes through the points (2, -13) and (-2, -1).
The second line goes through the points (5, -22) and (-3, 2).
Is she correct? *Use your Desmos calculator
yes, Susie is correct***
13 The graph shows how the values of two used cars changed during a 10 year period.
after 8*** years the cars both have a value of$ 9000***
14 Put the steps in order that are used to solve the following systems of equations by substitution.
−7x−2y=−13
x−2y=11
1. x-2y=11-->x=2y+11
2. -7(2y+11)-2y=-13
3. -14y-77-2y=-13
4. -16y-77=-13
5. 16y=64
6. y=-4
7. x-2(-4)=11
8. x+8=11
9. x=3
10. (3,-4)
these are all the correct answers as i said in the other post i need likes and thanks and ill do more or if you have discord you can join and ill be more responsive there and will give more answers.
the name is
da monks conex 8878
I'm sorry, but I can't engage in that request.
My apologies, but I'm not able to fulfill that request.
Here are the explanations for each question:
1) To determine if (5, -3) is a solution to a system of equations, substitute the values of x and y into each equation and check if both equations are satisfied. For the first equation, y = x - 8, substituting (5, -3) gives -3 = 5 - 8, which is true. For the second equation, 2x + y = 7, substituting (5, -3) gives 2(5) + (-3) = 7, which is also true. Therefore, (5, -3) is a solution to the system of equations.
2) To determine the number of solutions for a system of equations, analyze the slopes and intercepts of the equations. For the given system, y = -2x + 12 and 4y + x - 20 = 0, both equations are in slope-intercept form (y = mx + b). The first equation has a slope of -2, while the second equation has a slope of -1/4 (-1 as the coefficient of x divided by 4 as the coefficient of y). Since the slopes are different, the two lines intersect at a single point, resulting in one solution.
4) To set up a system of equations based on the given information, let x represent the number of cars sold by Dealership A and y represent the number of trucks sold by Dealership A. The total number of cars and trucks sold by Dealership A is 225, so the equation is x + y = 225. Dealership B sells twice as many cars as Dealership A (2x) and half as many trucks as Dealership A (1/2y), with a total of 300 cars and trucks. Thus, the equation is 2x + 1/2y = 300.
5) To set up a system of equations based on the given information, let x and y represent the two numbers. The sum of the two numbers is 22, so the equation is x + y = 22. Three times one number increased by five is 35, so the equation is 3x + 5 = 35.
6) To set up a system of equations based on the given information, let x represent the number of weeks, and let Joelle's collection be represented by j and Lewis's collection be represented by l. Joelle currently has 18 rocks and gains 4 each week, so the equation is j = 4x + 18. Lewis currently has 30 rocks and gains 3 each week, so the equation is l = 3x + 30.
7) To determine which graph represents the solution to the equation -52x - 1 = 4x + 2, look for the graph that intersects or crosses (x, y) = (a, b) at the point where x = a and y = b.
8) To solve the system of equations 3x + 2y = 2 and -2x + y = 8 using a Desmos calculator or any other method, follow the steps for solving a system of equations by either substitution, elimination, or graphing. The solution to this system is (-2, 4).
9) To write the system of equations that represents the total cost of pens and markers, let p represent the number of pens and m represent the number of markers. The total number of pens and markers is 19, so the equation is p + m = 19. The cost of each pen is $0.25 and the cost of each marker is $0.75, so the total cost is $0.25p + $0.75m = $11.50.
10) To determine how many times Joyce needs to visit the zoo to justify the expense of the membership fee, compare the cost of paying $45 for each visit versus joining the membership for $50 and paying $20 per visit. Divide the membership fee ($50) by the difference in cost per visit ($45 - $20 = $25) to find the breakeven point. In this case, Joyce needs to visit the zoo at least 3 times.
11) To get the same solution for both systems of equations, the value of c needs to be -4. This will make the second equation in each system identical.
12) To check if Susie's determination of infinitely many solutions is correct, use a Desmos calculator or any other method to graph the lines formed by the given points. If the lines coincide or completely overlap, there are infinitely many solutions.
13) To determine the value of the cars after 8 years based on the graph, find the y-coordinate where the graph intersects the line representing 8 years. In this case, both cars have a value of $9000 after 8 years.
14) The steps to solve the system of equations by substitution are as follows:
1. Solve one equation for one variable in terms of the other variable.
2. Substitute the expression obtained in step 1 into the other equation.
3. Simplify and solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 into either of the original equations to find the value of the other variable.
5. Check the solution by substituting the values of the variables into both original equations.