Graphing
In a graph, lines intersect at how many points? How many solutions?
One for both
1 solution
Solve using Substitution:
y=x-3 and y=2x
(-3,-6)
Solve using elimination:
4x-y=-8
7x+y=-14
(-2, 0)
Write and solve a system of equation for each situation AND interpret the solution.
The sum of two numbers is 20.5. Their difference is 6.5. Find the two numbers.
(13.5, 7)
When graphing, what direction do you go for a positive number up or down? What direction do you go for a negative number up or down?
Positive=up
Negative=down
When you have the SAME line and slope, what type of solution is this?
Infinite
Solve using Substitution:
y=-6+x and y=3x
(-3, -9)
Solve using elimination:
2x+5y=3
4x-5y=21
(4, -1)
Write and solve a system of equation for each situation AND interpret the solution.
Tadeo volunteered at the library 6 times as many hours over the weekend as Dylan. Together they volunteered a total of 14 hours. How many hours did each person volunteer over the weekend?
(2, 12) Tadeo volunteered 12 hours and Dylan 2 hours
Graph the following equation and show Mrs. Alter your graph. (do on graph paper)
x=3 and y=-6
After graphing give the solution.
Graph: x=3 should be a vertical (up/down)line on the positive 3 and y=-6 should be a horizontal line (straight across) on the -6.
Solution is (3, -6)
When you have the SAME slope but a DIFFERENT line what type of solution is this?
No Solution
Solve using Substitution:
-3x+4y=6
-x+2y=8
(10, 9)
Solve using elimination:
x+2y=-1
7x-3y=10
(1, -1)
Write and solve a system of equation for each situation AND interpret the solution.
Mrs. Adesso wants to take her class on a trip to either the science center or natural history museum. The Science center charges $7 per student, plus $75 for a guided tour. The natural history museum charges $8 per student plus $50 for a guided tour. For what number of students is the cost of the trip the same at each museum?
25 students the cost is $250 (25, 250)
y=2/3x+1
y-2/3x=-3
*Hint you will need to switch one of the equations for it to say y=
No solution, lines are parallel
A system of equations consists of 2 lines. A line passes through EACH pair of points. Determine whether the line through the first pair of points intersects through the second pair of points:
(0, -5) and (2, -4)
(4, -3) and (6, -2)
Does intersect
Solve using Substitution:
y+7=2x
2y=4x-14
Solve using elimination:
2x+5y=-13
x+3y=-5
(-14, 3)
Write and solve a system of equation for each situation AND interpret the solution.
At a farmer's market, Amar purchased 4 jars of salsa and 3 cucumbers and spent a total of $12.25. Dylan purchased 1 jar of salsa and 2 cucumbers and spent a total of $4. Dakota purchased 1 jar of salsa and 5 cucumbers. If each jar of salsa costs the same and each cucumber costs the same, how much did Dakota spend?
$6.25
y+1/3x=1
y=-1/3x+1
A system of equations consists of 2 lines. A line passes through EACH pair of points. Determine whether the line through the first pair of points intersects through the second pair of points:
(0, 4) and (1, 7)
(-1, -5) and (5, 13)
Does NOT intersect
Solve using Substitution:
9x+y=9
y+9x=5
No solution
Solve using elimination:
The cost of 8 muffins and 2 quarts of milk is $18. The cost of 3 muffins and 1 quart of milk is $7.50. This situation can be represented with the system 8x+2y=18 and 3x+y=7.50, where x represents the cost of each muffin and y represents the cost of one quart of milk. Find the cost of the muffin and quart of milk.
$1.50 for each muffin and $3 for a quart of milk
Write and solve a system of equation for each situation AND interpret the solution.
The table shows the number of days and total number of miles Sydney ran and cycled each week. Each day that she ran, she ran the same number of miles. Each day that she cycled, she cycled the same number of miles. Complete the table to find the total number of miles Sydney ran and cycled in Week C.
Week #Days Ran #Days Cycled Total Miles
A 2 3 40
B 3 4 55
C 4 2
40 miles