At a restaurant mike and his three friends decide to divide the bill evening. If each person paid 13 then what was the total bil
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Answer:
1. The equation is solved by the graphed systems of equations is:
Third option: 7x + 3 = x − 3
2. The solution to the system is:
Fourth option: (3,-1)
3. The graph of the system y = −2x + 3 and 2x + 4y = 8 is:
Third option: Line through point (0, 3) and (1, 1). Line through (0, 2) and (4, 0).
4. The solution to the system is:
Second option: Infinite solutions.
5. Bill will have read the same amount of books as Mandy in:
Fourth option: December
Step-by-step explanation:
Question 1. What equation is solved by the graphed systems of equations?
Two linear equations that intersect at the point (-1, -4)=(x,y)→x=-1, y=-4
a. 7x + 3 = x + 3
Solving for x: Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:
7x+3-x=x+3-x
6x+3=3
Subtracting 3 both sides of the equation:
6x+3-3=3-3
6x=0
Dividing both sides of the equation by 6:
6x/6=0/6
Dividing:
x=0 different to the intersection at x=-1, then this is not the equation.
b. 7x − 3 = x − 3
Solving for x: Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:
7x-3-x=x-3-x
6x-3=-3
Adding 3 both sides of the equation:
6x-3+3=-3+3
6x=0
Dividing both sides of the equation by 6:
6x/6=0/6
Dividing:
x=0 different to the intersection at x=-1, then this is not the equation.
c. 7x + 3 = x − 3
Solving for x: Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:
7x+3-x=x-3-x
6x+3=-3
Subtracting 3 both sides of the equation:
6x+3-3=-3-3
6x=-6
Dividing both sides of the equation by 6:
6x/6=-6/6
Dividing:
x=-1 equal to the intersection at x=-1, then this is the equation.
d. 7x − 3 = x + 3
Solving for x: Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:
7x-3-x=x+3-x
6x-3=3
Adding 3 both sides of the equation:
6x-3+3=3+3
6x=6
Dividing both sides of the equation by 6:
6x/6=6/6
Dividing:
x=1 different to the intersection at x=-1, then this is not the equation.
Question 2 (Multiple Choice Worth 2 points) (06.03) Solve the system 2x + 3y = 3 and 3x − 2y = 11 by using graph paper or graphing technology. What is the solution to the system?
The solution to the system is (3, -1) Fourth option
Please, see the attached graph.
Question 3 (Multiple Choice Worth 2 points) (06.03) What is the graph of the system y = −2x + 3 and 2x + 4y = 8?
Third option: Line through point (0, 3) and (1, 1). Line through (0, 2) and (4, 0).
Please, see the attached graph.
Question 4 (Multiple Choice Worth 2 points) (06.03) Solve the system y = 3x + 2 and 3y = 9x + 6 by using graph paper or graphing technology. What is the solution to the system?
Second option: Infinite solutions.
Please, see the attached graph.
Question 5 (Multiple Choice Worth 2 points) (06.03) At the end of April, Mandy told Bill that she has read 16 books this year and reads 2 books each month. Bill wants to catch up to Mandy. He tracks his book reading with a table on his door. Using his table below, what month will Bill have read the same amount of books as Mandy?
Bill
Month Books
May 4
June 8
July 12
August 16
September 20
October 24
November 28
December 32
Books read by Mandy: y=16+2x
Numbers of months since april: x
May: x=1→y=16+2(1)=16+2→y=18 different to 4 (books read by Bill)
June: x=2→y=16+2(2)=16+4→y=20 different to 8 (books read by Bill)
July: x=3→y=16+2(3)=16+6→y=22 different to 12 (books read by Bill)
September: x=5→y=16+2(5)=16+10→y=26 different to 20 (books read by Bill)
October: x=6→y=16+2(6)=16+12→y=28 different to 24 (books read by Bill)
November: x=7→y=16+2(7)=16+14→y=30 different to 28 (books read by Bill)
December: x=8→y=16+2(8)=16+16→y=32 equal to 32 (books read by Bill)
Answer. Fourth option: December
To find the equation of a line in slope-intercept form given two points, we must arrange the points this way to find the slope (
):
We can replace the variables in this equation with the values from the points we have been given, (
) and (2, 14). We know that the x-values always come first in an ordered pair, so we can put those in our equation first.
It doesn't really matter which x-value goes in which x-value slot in the equation as long as you match up the y-values in the same fashion. But for the sake of convenience, we will call the 2 in the second ordered pair
and the 
in the first ordered pair 
.
Now, we can match these values in our equation, and while we're at it, we can substitute the appropriate y-values into their places as well.
Now, we can see that we are subtracting negatives in this equation. Remember that whenever you subtract a negative, it is the same as adding a positive. So, this equation could be rewritten as
and we can change the improper fraction in the numerator into a mixed number for ease of addition.
And here, we can add, since it's made simple for us.
Finally, to get the slope we can complete the fraction by dividing.
The slope of this equation,, is 7, and so far, our equation looks like this:
Now, to find y-intercept.
To do this, we simply have to substitute one of the ordered pairs in for the appropriate x- and y-values and solve. To make it easier on ourselves, we can use (2, 14) so we don't have to deal with negative numbers or fractions.
Let us substitute in our values.
Now, we can solve by multiplying the 7 and 2.
Here, we can subtract 14 from both sides, since it is added to both in the equation, and we are left with
which can be flipped around to show
The y-intercept of this line is 0.
Now, we can make this known in our equation like this:
Or, for neatness' sake, we can just say
which is your final equation.
The line through () and (2, 14) in slope-intercept form is <span>.
Hope that helped! =) </span>
We can replace the variables in this equation with the values from the points we have been given, (
It doesn't really matter which x-value goes in which x-value slot in the equation as long as you match up the y-values in the same fashion. But for the sake of convenience, we will call the 2 in the second ordered pair
Now, we can match these values in our equation, and while we're at it, we can substitute the appropriate y-values into their places as well.
Now, we can see that we are subtracting negatives in this equation. Remember that whenever you subtract a negative, it is the same as adding a positive. So, this equation could be rewritten as
and we can change the improper fraction in the numerator into a mixed number for ease of addition.
And here, we can add, since it's made simple for us.
Finally, to get the slope we can complete the fraction by dividing.
The slope of this equation,
Now, to find y-intercept.
To do this, we simply have to substitute one of the ordered pairs in for the appropriate x- and y-values and solve. To make it easier on ourselves, we can use (2, 14) so we don't have to deal with negative numbers or fractions.
Let us substitute in our values.
Now, we can solve by multiplying the 7 and 2.
Here, we can subtract 14 from both sides, since it is added to both in the equation, and we are left with
which can be flipped around to show
The y-intercept of this line is 0.
Now, we can make this known in our equation like this:
Or, for neatness' sake, we can just say
which is your final equation.
The line through (
Hope that helped! =) </span>