System of Equations
System of Equations
Tranformations
Random Choice
Random Choice
100
- Enter the value for x that makes the equation 2(x – 3) + 21 = -3 true.
x= -9
100
Select the value of n that makes the equation true.
2 (4n + 2 )= 20
A.n = 2
B. n = 3
C. n = 2.25
D. n = 2.75
A. n=2
100
Look at rectangle QRST on the coordinate plane.
Which coordinate plane shows Q'R'S'T', the image of QRST after a rotation of 180 degrees about the origin?
C.
100
What solution(s) does the system of equations have?
-2x+5y= 10
-4x + 10y = 20 .
a. There are infinitely many solutions.
b. The only solution is (5, 4).
c. The only solution is (10, 6).
d. There are no solutions.
a. There are infinitely many solutions.
100
Two lines tlfat have the different slopes intersect at exactly one point.
a. True for all cases
b. True for some cases
c. Not True for any cases
a. True for all cases
200
Enter the value of x that makes the following equation true?
1/2x +2=3/4x
x=8
200
A system of two linear equations has infinitely many solutions. One equation is x-4y = 5. Select the equation that would make this system have infinitely many solutions.
a. x+4y= 5
b. x-4y=7
C. -4y+x= 3
d. 4y-x=-5
d. 4y-x=-5
200
Rectangle PQRS is graphed on a coordinate plane with vertices P −2, 1 , Q −2, 4 , R −4, 4 , and S −4, 1 , as shown below.
Rectangle PQRS is reflected over the y-axis and then translated 2 units to the left resulting in Rectangle P′Q′R′S′. What are the coordinates of P′?
A.−4, − 1
B. 0, 1
C. 1, 0
D. 4, 1
B. 0, 1
200
The graph shown compares the amount of money Mark (M) and Gloria (G) are saving. How many weeks after Mark started saving did Gloria have the same amount of money as Mark?
Enter the time, in weeks, when Mark and Gloria had the same amount of money.
5 weeks
200
Two lines that have the same y-intercept and the same slope intersect at exactly one point.
a. True for all cases
b. True for some cases
c. Not True for any cases
c. Not True for any cases
300
Which equation has no solution?
A. x = 2
B. 4x + 2 = 10
C. 4x = 4x
D. 3x + 2 = 3x – 1
D. 3x+ 2= 3x-1
300
7. What is the solution to this system of equations?
3x + 2y = − 10
y = − x − 4
A.− 2, − 2
B. − 2, 2
C. − 18, 14
D. no solution
A. ( -2, -2)
300
In ∆DEF, ∠DEF measures 30 ̊, ∠EFD measures 60 ̊, and ∠FDE measures 90 ̊.
Suppose the triangle were reflected across the line
y = –x in a coordinate plane.
Which of these statements would be correct about the
resulting triangle?
A. ∠E'F'D' would measure 60 ̊
B. ∠D'E'F' would measure 90 ̊
C. ∠F'D'E' would measure 60 ̊
D. ∠E'F'D' would measure 30 ̊
A. <E'F'D' would measure 60 degree.
300
Which of these statements is true about the two trapezoids graphed below?
A.They are congruent, because one can be obtained by translating the other 6 units to the right and 7 units down.
B. They are congruent, because one can be obtained by translating the other 7 units to the right and 6 units down.
C. They are not congruent, because one can be obtained by translating the other 6 units to the right and 7 units down.
D. They are not congruent, because one can be obtained by translating the other 7 units to the right and 6 units down.
A.They are congruent, because one can be obtained by translating the other 6 units to the right and 7 units down.
300
Which of these statements is true about the two graphed parallelograms?
A. They are similar, because one can be
obtained by dilating the other about the
origin with a scale factor of 1/4
.
B. They are similar, because one can be
obtained by dilating the other about the
origin with a scale factor of 1/2
.
C. They are not similar, because one can be
obtained by dilating the other about the
origin with a scale factor of 1/4
.
D. They are not similar, because one can be
obtained by dilating the other about the
origin with a scale factor of 1/2
.
B. They are similar, because one can be
obtained by dilating the other about the
origin with a scale factor of 1/2
400
Estimate the solution of the linear system graphically and check the solution algebraically:
x + y = − 13
x − y = 5
B. (1, -2)
400
A system of two linear equations is shown.
5x + 2y = – 4
5x + 2y = 1
Which statement is true regarding the solution to this system of linear equations?
A. The system has no solution because the lines are parallel.
B. The system has no solution because the equations represent the same line.
C. The system has an infinite number of solutions because the lines are parallel.
D. The system has an infinite number of solutions because the equations represent the same line.
A. The system has no solution because the lines are parallel.
400
Rectangle RSTU is shown on the coordinate plane below.
Rectangle RSTU is rotated 90˚ counterclockwise about the origin to produce rectangle R'S'T'U'.
What the length, in units, of S’T’?
7 units
400
Which of the following transformation sequences will transform figure TUVW into figure T’U'V'W'?
A. A reflection over the y-axis followed by a 180˚ clockwise rotation about the origin.
B. A reflection over the x-axis followed by a 90˚ clockwise rotation about the origin.
C. A reflection over the x-axis followed by a translation of 3 units to the right and 1 unit down.
D. A translation of 3 units to the right and 5 units down.
C. A reflection over the x-axis followed by a translation of 3 units to the right and 1 unit down.
400
There are 25 coins inside a container. Some of the coins are nickels, and the rest are quarters. The value of the coins is $4.05. Let n represent the number of nickels, and let q represent the number of quarters. Which system of equations represents this situation?
a. t-q=25
0.05n + 0.25q = 4.05
b. t+q= 4.05
0.05n + 0.25q == 25
C. t+q=25
0.05n + 0.25q == 4.05
d. t+q == 25 .
Sn+ !5q = 4.05
C. t+q=25
0.05n + 0.25q == 4.05
500
Yesenia currently exercises at X-Fitness. The cost to exercise there is $5 per day. She is considering switching to Work-Out-Now. Work-Out-Now has a membership start-up fee of $40; after the start-up fee, the cost to exercise there is $3 per day. How many days, d, will Yesenia have to exercise for the price of Work-Out-Now to be the same as X-Fitness?
20 days
500
Tara places a picture in a picture frame. The width of the picture is x inches, and the length of the picture is 2 inches more than the width. The frame is 1 inch wide on all sides. The perimeter of the outside of the picture frame is 28 inches. Tara writes the equation below to find the width, in inches, of the picture.
2 (x + 2 )+ 2 (x + 4)= 28
What is the width, in inches, of the picture?
4 inches
500
Peter claims that the two figures are congruent since Figure 2 can be obtained by translating Figure 1 to the left and then rotating it clockwise around point P.
How many degrees must the rotation be in order for Peter's claim to be correct? Enter the smallest possible degree measure.
180 degrees
500
A sequence of transformations is applied to a polygon. Which of the following statements represent a sequence of transformations where the resulting polygon is similar to the original polygon but has a smaller area than the original polygon? Select ALL that apply
A. a reflection over the y-axis followed by a translation of 10 units down and a dilation about the origin by a scale factor of 2
B. a rotation of 180° counterclockwise about the origin followed by a dilation about the origin by a scale factor of 5/2
C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left
D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y-axis and a dilation about the origin by a scale factor of 3/4
C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left
D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y-axis and a dilation about the origin by a scale factor of 3/4
500
Does the ordered pair (-5, 3) satisfy the system of equations? Explain.
y= -2x-1
y= -3/5x
a. Yes, because the ordered pair (-5, 3) satisfies both equations of the system.
b. No, because the ordered pair (-5, 3) satisfies only the equation y = -2x- 1.
c. No, because the ordered pair (-5, 3) satisfies only the equation y = -¾x.
d. No, because the ordered pair (-5, 3) satisfies neither equation of the system.
c. No, because the ordered pair (-5, 3) satisfies only the equation y = -¾x.