Graphing Systems
Solve the system of equations by graphing:
y=-1/4x + 6 and y=1/2x + 3
(4, 5)
Graph: y > 1/2x + 2 and x< -3
Dashed line and above
Solve the system of equations using the substitution method: x= 3 and 5x + y = 1
(3,-14)
Solve the system of equations using the elimination method:
x + y= 11 and x - y= -3
(4, 7)
The school faculty has found out they aren’t able to get the same size tables for a school dance. The rental company has let them know that they are able to receive some tables that will fit 8 students and some tables will fit 9 students. If a total of 111 students are planning to attend the dance and the school has ordered 13 tables, then how many tables were ordered that fit 9 students?
7
Solve the system of equations by graphing:
y=1/2x + 1 and y=4
(6, 4)
Graph: y < 5x - 6 & y > x
Dashed line and below
Solve the system of equations using the substitution method: x= y - 3 and 5x + 3y = 1
(-1, 2)
Solve the system of equations using the elimination method:
3x + 2y = 0 and -3x + y= 9
(-2, 3)
Billy, a 5th grader, has decided that he would like a summer job. He decides that he will be selling lemonade for $4 and ice tea for $3. If he sold a total of 21 drinks for $76, then how many lemonades did he sell?
13
Solve the system of equations by graphing:
y=-3x + 4 and 2x -y=1
(1, 1)
DOUBLE JEOPARDY!!!
Graph: y <= -3/2x - 1 & y>= -3/2x +4
Solid Line and Below
Solve the system of equations using the substitution method: 3x - y= 7 and y= 2x - 4
(3, 2)
Solve the system of equations using the elimination method:
6x - 2y= 36 and 3x - 2y= 21
(5, -3)
DOUBLE JEOPARDY!!!
Gaby and Danny are at Hamburger and Shakes restaurant. Hamburgers cost $4.50 and shakes cost $2.50. If Gaby and Danny bought a total of 12 items for $42, how many shakes did they buy?
6
Solve the system of equations by graphing:
y=-2/5x +4 and y=-2/5x+1
No solution; parallel lines
Graph:
y<1/2x and y>3x + 10
Intersects at (-4, -2)
Solve the system of equations using the substitution method: x= 12 + 3y and 2x + 5y= -20
(0, -4)
Solve the system of equations using the elimination method:
3x + y= -11 and 4x - 3y= 7
(-2, -5)
The drama club is running a lemonade stand to raise money for its new production. A local grocery store donated cans of lemonade and bottles of water. Cans of lemonade sell for $2 each and bottles of water sell for $1.50 each. The club needs to raise at least $500 to cover the cost of renting costumes. The students can accept a maximum of 360 cans and bottles. Write a system of inequalities that can be used to represent this situation.
2x + 1.50y >= 500
x + y <= 360
Solve the system of equations by graphing:
y=1/2x+1 and y=3/2x-5
(6, 4)
Graph the system of inequalities:
y<-2x +3 and y > 3
Intersects at (0, 3)
Solve the system of equations using the substitution method: 2x + 3y = 17 and y = -2x+3
(-2, 7)
DOUBLE JEOPARDY!!!
Solve the system of equations using the elimination method:
3x + 4y= -25 and 2x - 3y= 6
(-3, -4)
At a dance recital, there were 100 student dancers performing. If there were 20 more girls than boys, how many boys were performing?
40