ACT 1 Alg: Solve systems of 2 equations in 2 variables

Welcome to your ACT 1 Alg: Solve systems of 2 equations in 2 variables

$Q1:$ At a museum, Nour bought 3 student tickets and 2 adult tickets for $29.00£$. At the same museum Sara bought 5 student tickets and 4 adult tickets for $54.00£$. How much does one student ticket and one adult ticket cost?

$12.5£$

$12£$

$11.5£$

$11£$

$Q_{2}:$ On the second weekend of May, Anna hiked 10 less than twice the number of miles that she hiked on the first weekend of May. In these two weeks she hiked a total of 38 miles. How many miles did she hike on the first weekend?

$38$

$16$

$48$

$10$

$Q_{3}:$ Ahmad and Mohammad purchased a printer together for $258. If Ahmad paid 18£ less than twice Mohammad, how much money did Ahmad pay for the printer?

$172$

$166$

$158$

$146$

$Q_{4}:$ There are 28 tables for customers at Grill Restaurant. The tables are either two-seat tables or four-seat tables. When all the tables are full, there will be 90 customers in the restaurant. How many two-seat tables are at the restaurant?

$11$

$13$

$15$

$17$

$Q_{5}:$ In a basketball, a field goal is either 2 or 3 points. In a college basketball tournament, Ahmad made 73 more 2-point field goals than 3-point field goals. If he scored a total of 216 goals in the tournament how many 3-point field goals did he make?

$12$

$14$

$16$

$18$

$Q_{6}:$ In a car dealership, all of the vehicles are either a sedan or a SUV. If 36 sedans are sold and 36 SUVs are added, there will be an equal number of sedans and SUVs. If 8 SUVs are sold and 8 sedans are added, there will be twice as many sedans as SUVs. How many sedans were at the dealership before any vehicle was sold?

$132$

$144$

$156$

$168$

$Q_{7}:$ At a coffee shop, a $16$ ounce bag of coffee is on sale at $5.25£$ less than the regular price. The cost of $ 4$ bags of coffee at regular price is the same as the cost of $6$ bags of coffee at sale price. Let $r$ be the regular price of coffee and $s$ be the sale price of coffee. Which of the following systems of equations can be used to find the values of variables $r$ and $s$ ?

$s=r-16$, $r=6s$

$s=r-5.25$, $4r=16$

$s=r-16$, $4r=6s$

$s=r+5.25$, $4r=6s$

$Q_{8}:$ One section of a grocery store display only water bottles. The water bottles are in either 6-bottle packages or 8-bottle packages. Let x represent the number of 6-bottle packages and y represent the number of 8-bottle packages. The total number of packages displayed are 270 and the total number of bottles are 1,860. To find the values of variables x and y, which of the following systems of equations can be used?

$x+y=1860$, $6x+8y=270$

$6x+8y=1860$, $x+y=270$

$8x+6y=1860$, $x+y=270$

$x+y=1860$, $8x+6y=270$

$Q_{9}:$ Carl drove from his home to the beach at an average speed of 50 mph and returned home along the same route at an average speed of 30 mph. His total driving time for the trip was 2 hours. Solving which of the following systems of equations yields, x , the time it took for Carl to drive to the beach and, y , the time spent for the return trip?

$x=y+2$, $50x=30y$

$x+y=2$, $30x=50y$

$x+y=2$, $50x=30y$

$y=x+2$, $30x=50y$

$Q_{10}:$ The solution of the system of $2x+y=13$ and $3x-y=12$ is

$x=-5$, $y=-3$

$x=5$, $y=-3$

$x=-5$, $y=3$

$x=5$, $y=3$

$Q_{11}:$ The solution of the system of $2x+3y=31$ and $3x+2y=29$ is

$x=5$, $y=7$

$x=5$, $y=-7$

$x=-5$, $y=7$

$x=5$, $y=7$

$Q_{12}:$ One of the solution of the system of $y=2x-1$ and $y=x^{2}-2x+2$ is

$x=-1$, $y=1$

$x=3$, $y=5$

$x=1$, $y=-1$

$x=3$, $y=-5$

$Q_{13}:$ If the sum of two numbers is 13 and the difference of the numbers is 23, what is the product of the numbers?

$-90$

$-23$

$0$

$18$

$Q_{14}:$ The system of equations given by $2x + 3y = 7$ and $10x + cy = 3 $ has solutions for all values of $c$ EXCEPT

$15$

$-3$

$3$

$10$

$Q_{15}:$ If x and y are real numbers such that $3x + 4y = 10$ and $2x − 4y = 5$, then what is the value of $x$ ?

$4$

$6$

$3$

$15$

$Q_{16}:$ If $12a − 3b = 131$ and $5a − 10b = 61$, then what is the value of $a + b$ ?

$10$

$70$

$7$

$50$

$Q_{17}:$ If $4n − 8m = 6$, and $−5n + 4m = 3$, then $n =$

$7$

$-7$

$2$

$-2$

$Q_{18}:$ If $a + 3b = 6$, and $4a − 3b = 14$, then $a=$

$-4$

$2$

$4$

$10$

$Q_{19}:$ If $2x − 7y = 12$ and $−8x + 3y = 2$, which of the following is the value of $x − y $?

$12$

$8$

$5.5$

$1$

$Q_{20}:$ The solution of the system of $x+4y=5$ and $-5x+-20y=29$ is

$x=3$, $y=4$

$x=5$, $y=-2$

$x=-2$, $y=7$

No solution

$Q_{21}:$ The solution set to the pair of equations: $mx + ny = 15 $, $nx + my = 13$ is $x = 3$ and $y = 1$. What are the values of $m $ and $n$?

$m,n=5,3$

$m,n=4,3$

$m,n=3,4$

$m,n=3,5$

$Q_{22}:$ What are the coordinates of the point of intersection of the lines having the following equations: $x-\sqrt{3y}=\sqrt{3}$, $\sqrt{3x}+y=1$

$(\frac{-1}{2},\frac{-\sqrt{3}}{2})$

$(\frac{-2\sqrt{3}}{3}, \frac{-1}{2})$

$(\frac{1}{2},\frac{2}{\sqrt{3}})$

$(\frac{3}{2\sqrt{3}},\frac{-1}{2})$

$Q_{23}:$ The solution of the system of $y=8x-14$ and $y=x$ is

$x=-7$, $y=-7$

$x=7$, $y=7$

$x=2$, $y=2$

$x=-2$, $y=-2$

$Q_{24}:$ The solution of the system of $2y=x+36$ and $y=\frac{1}{2}x+4$ is

$x,y=0,-2$

$x,y=5,-2$

$x,y=0,2$

No solution

$Q_{25}:$ The solution of the system of $6x -2y= 18$ and $-6x +2y= -18$ is

$x=-3$, $y=-3$

$x=4$, $y=-4$

Infinitely many solutions

No solution

$Q_{26}:$ Tickets for the homecoming football game cost $3£$ for students and $5£$ for the general public. Ticket sales totaled $1,396£$, and 316 people attended the game. How many student tickets were sold?

$244$

$92$

$180$

$540$

$Q_{27}:$ A mother is twice as old as her daughter. Twelve years ago she was three times as old as her daughter was then. Find the mother’s present age.

$48$

$24$

$36$

$100$

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