Solve the system by graphin -2x=2y-4 2x-y=-5
To solve the system of equations by graphing, we need to graph the equations on the same coordinate plane and find the point of intersection.
For the first equation, -2x=2y-4, we can rewrite it in slope-intercept form as y = -x + 2. Let's create a table of values and graph it:
x | y
------
0 | 2
1 | 1
2 | 0
Plotting these points and drawing a line through them, we get:
Graph of -2x=2y-4 or y = -x + 2:
{{{graph(300,300,-5,5,-5,5,-x+2)}}}
Now let's graph the second equation, 2x-y=-5. Rearranging it in slope-intercept form, we have y = 2x + 5. We can create another table of values and graph it:
x | y
------
0 | 5
1 | 7
2 | 9
Plotting these points and drawing a line through them, we get:
Graph of 2x-y=-5 or y = 2x + 5:
{{{graph(300,300,-5,5,-5,10,2x+5)}}}
Now we can see that the lines intersect at the point (1, 1). Therefore, the solution to the system of equations is x = 1 and y = 1.
4.3.7 - Quiz: Systems of Inequalities Quiz Part 1
I apologize, but I'm unable to generate or provide quizzes. However, if you have any specific questions or need help with systems of inequalities, I would be more than happy to assist you.
A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 per day to rent the same car.Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day.
To find the number of days for which the costs are the same, we can set up an equation.
For the first rental car agency, the cost is $110.00 + $46.00 per day: C1 = 110 + 46d, where d represents the number of days.
For the second rental car agency, the cost is $70.00 + $54.00 per day: C2 = 70 + 54d.
We want to find the value of d when C1 = C2. So we set up the equation:
110 + 46d = 70 + 54d
To solve this equation, we can subtract 70 from both sides:
40 + 46d = 54d
Now, subtract 46d from both sides:
40 = 8d
Divide both sides by 8:
5 = d
Therefore, the costs are the same after approximately 5 days.
Which point is a solution to the following system of inequalities?enlarged left brace start layout 1st row negative 2 x plus 3 y greater than 1 2nd row negative 5 x plus 6 y less than or equal to 1 end layout(1 point)Responsesleft parenthesis 6 comma 6 right parenthesisImage with alt text: left parenthesis 6 comma 6 right parenthesis835241,left parenthesis 7 comma 8 right parenthesisImage with alt text: 835241,left parenthesis 7 comma 8 right parenthesisleft parenthesis 8 comma 7 right parenthesisImage with alt text: left parenthesis 8 comma 7 right parenthesisleft parenthesis 9 comma 7 right parenthesis
To determine which point is a solution to the system of inequalities:
-2x + 3y > 1
-5x + 6y ≤ 1
We can test each point by substituting the x and y values into the inequalities to see if they hold true.
Let's test each point:
1. (6, 6)
Plugging in x = 6 and y = 6 into the inequalities:
-2(6) + 3(6) > 1 -> -12 + 18 > 1 -> 6 > 1 (True)
-5(6) + 6(6) ≤ 1 -> -30 + 36 ≤ 1 -> 6 ≤ 1 (False)
Since the second inequality does not hold true, (6, 6) is not a solution to the system of inequalities.
2. (7, 8)
Plugging in x = 7 and y = 8 into the inequalities:
-2(7) + 3(8) > 1 -> -14 + 24 > 1 -> 10 > 1 (True)
-5(7) + 6(8) ≤ 1 -> -35 + 48 ≤ 1 -> 13 ≤ 1 (False)
Since the second inequality does not hold true, (7, 8) is not a solution to the system of inequalities.
3. (8, 7)
Plugging in x = 8 and y = 7 into the inequalities:
-2(8) + 3(7) > 1 -> -16 + 21 > 1 -> 5 > 1 (True)
-5(8) + 6(7) ≤ 1 -> -40 + 42 ≤ 1 -> 2 ≤ 1 (False)
Since the second inequality does not hold true, (8, 7) is not a solution to the system of inequalities.
4. (9, 7)
Plugging in x = 9 and y = 7 into the inequalities:
-2(9) + 3(7) > 1 -> -18 + 21 > 1 -> 3 > 1 (True)
-5(9) + 6(7) ≤ 1 -> -45 + 42 ≤ 1 -> -3 ≤ 1 (True)
Since both inequalities hold true, (9, 7) is a solution to the system of inequalities.
Therefore, the point (9, 7) is a solution to the system of inequalities.
Solve the system of inequalities by graphing.y is less than or equal to negative four x minus one and y is greater than three x minus one(1 point)Responsesanswer option aThe point of intersection is left-parenthesis 0 comma negative 1 right-parenthesis. The first line goes through left-parenthesis negative 1 comma 3 right-parenthesis and left-parenthesis 0 comma negative 1 right-parenthesis. The second line is dotted and goes through left-parenthesis 0 comma negative 1 right-parenthesis and left-parenthesis 1 comma 2 right-parenthesis. The graph is shaded to the right of the first line and to the left of the dotted line.Image with alt text: answer option a The point of intersection is left-parenthesis 0 comma negative 1 right-parenthesis. The first line goes through left-parenthesis negative 1 comma 3 right-parenthesis and left-parenthesis 0 comma negative 1 right-parenthesis. The second line is dotted and goes through left-parenthesis 0 comma negative 1 right-parenthesis and left-parenthesis 1 comma 2 right-parenthesis. The graph is shaded to the right of the first line and to the left of the dotted line.answer option bThe point of intersection is left-parenthesis 0 comma negative 1 right-parenthesis. The first line goes through left-parenthesis 0 comma negative 1right-parenthesis and left-parenthesis 1 comma negative 5 right-parenthesis. The second line is dotted and goes through left-parenthesis 1 comma 2 right-parenthesis and left-parenthesis negative 1 comma negative 4 right-parenthesis. The graph is shaded to the right of the dotted line and to the left of the first line.Image with alt text: answer option b The point of intersection is left-parenthesis 0 comma negative 1 right-parenthesis. The first line goes through left-parenthesis 0 comma negative 1 right-parenthesis and left-parenthesis 1 comma negative 5 right-parenthesis. The second line is dotted and goes through left-parenthesis 1 comma 2 right-parenthesis and left-parenthesis negative 1 comma negative 4 right-parenthesis. The graph is shaded to the right of the dotted line and to the left of the first line.answer option cThe point of intersection is left-parenthesis 0 comma negative 1 right-parenthesis. The first line goes through left-parenthesis 0 comma negative 1 right-parenthesis and left-parenthesis 1 comma negative 5 right-parenthesis. The second line is dotted and goes through left-parenthesis 1 comma 2 right-parenthesis and left-parenthesis negative 1 comma negative 4 right-parenthesis. The graph is shaded to the left of the dotted line and to the left of the first line.Image with alt text: answer option c The point of intersection is left-parenthesis 0 comma negative 1 right-parenthesis. The first line goes through left-parenthesis 0 comma negative 1 right-parenthesis and left-parenthesis 1 comma negative 5 right-parenthesis. The second line is dotted and goes through left-parenthesis 1 comma 2 right-parenthesis and left-parenthesis negative 1 comma negative 4 right-parenthesis. The graph is shaded to the left of the dotted line and to the left of the first line.answer option d
The correct response is:
Answer option a:
The point of intersection is (0, -1). The first line goes through (-1, 3) and (0, -1). The second line is dotted and goes through (0, -1) and (1, 2). The graph is shaded to the right of the first line and to the left of the dotted line.
Image with alt text: The point of intersection is (0, -1). The first line goes through (-1, 3) and (0, -1). The second line is dotted and goes through (0, -1) and (1, 2). The graph is shaded to the right of the first line and to the left of the dotted line.