Heart of Algebra
Solve the systems of equations using substitution.
X=Y-3
2X-Y=-4
(-2,0)
Solve.
-6-(-9)/8
-15/8
What is the solution to the systems of equations?
X-3Y+3Z=-4
2X+3Y-Z=154X-3Y=z=19
(5,1,-2)
What is the slope for the following?
y=-4x
-4
A theatre group charges $12.50 per ticket for its opening play of the season. Production cost $150. What function could be used to determine the profit the theatre earns by selling (X) tickets?
f(x)=12.50x-150
Solve for X.
X-4Y=9
X=4Y+9
Write an equation to model the situation.
The product of 2 consecutive integers is 195?
n(n+2)=195
What is the solution for the systems of equations?
X=Y-3
X+3Y=13
(1,4)
What is the slope for the following equation?
Y=3/4X+763/4
A bank monthly charge for maintaining an account is $.45 for each check written plus a service fee charge of $12.50. If x represents the number of checks written during the month, What function models the situation?
f(x)=0.45x+12.50
Solve this system of equations for a and b.
a+2b=10
2a+b=6
a=2/3
b= 14/3
Write an equation to model the situation.
3 less than X is 25.X-3=25
A motel offers the specials shown. What does the motel charge per night?
Choice A: 3 nights and 1 meal for $250
Choice B: 3 nights and 6 meals for $330
$78.00
What is the equation for slope intercept form?
Y=mx+b
After all start up cost, a company starts with $100 and makes $.75 on each unit sold. Write the linear equation in slope intercept form that models this situation using p for profit and n for the units sold.
p=0.75n+100
At the farmer's market, a bag of apples and 3 cartons of strawberries cost $18.00 total. If the bag of apples cost 50% more than a carton of strawberries, how much does a bag of apples cost?
$6.00
Andy has won 12 out of the last 24 tennis matches he has played. If he wants to improve his winnings to 70% What would the equation be that could determine how many matches he would have to win in a row?
12+x/24+x=0.70
Last week Raul worked 11 more hours then Angle. If they worked a combined total of 59 hours, how many hours did Angle work?
24 hours
Which of the following represent b?
Y=3/4x+165
165
A theatre sells adult tickets for $8.00 and children's for $5.50. Sally bought some of each kind (not the same number) and paid a total of $78.50. What is the equation that represents this situation?
8x+5.5y=78.50
A cleaning company charges X dollars per hour to clean floors and Y dollars per hour to clean the rest of the house. When the company spends 2 hours to clean the floors and 3 hours to clean the rest of the house, the total charge is $80.00. When the company spends 1 hour clean floors and 4 hours to clean the rest of the house, the total charge is $100.00. Find out how much it would cost to clean the floors per hour.
$4.00
Eric took one hour to drive to the Phillips Arena and back. The return drive took 8 minutes less than the trip to the arena. if X represents the time it took Eric to drive from his apartment to the arena, what is an equation that you could use to determine how long he drove each way?
2X-8=60
Leroy invested $12,000 into two different bank accounts. One account (X) gives Leroy 1.5% interest yearly and the other account (Y) gives Leroy 3% interest yearly. At the end of one year Leroy had earned $300 in interest. What is a system of equations that cold be used to solve for how money Leroy invested in each account?
X+Y=12000
0.015X+0.03Y=300Who created slope intercept form?
Renee Descartes
A smart phone plan has a monthly base fee that includes 5 gigs of data. An overcharge is added when the 5 gigs are exceeded. The equation C=59+15(g-5) models the plan, where C is the monthly cost, in dollars, and g represents the total number of gigs used for the month. What does the value 59 represent in the equation given?
The base fee per month, in dollars, for the plan.