Vocabulary
The point where two lines cross.
What is the intercept/intersect.
Solve by graphing: y = x - 3 y = -x - 1
solution is (1,-2)
Solve by substitution: y = 2x, y = x + 5
Solution is (5, 10)
In solving by graphing, how many lines do you need to graph?
At least two.
Solve:
−4x − 2y = −12
4x + 8y = −24
What is (6, -6)
This is where you plot points of two lines to see where the two lines cross.
What is Solving by Graphing.
Solve by graphing: y = -2x - 1 y = x + 5
Solution is ( -2,3)
Solve by substitution: 2x + y = 5, y = x - 4
Solution is (3,-1)
How many different variables should be in your equation after you substitute an expression in for one of them?
One
When are you supposed to subtract two equations when solving using Elimination?
Give an example.
4x and 4x ; 4=4
Where you replace the variable in one equation with an expression from another equation. (a method)
What is solving by substitution.
Solve by graphing: y = 1/3x - 3, y = 4 - 2x
Solution is (3,-2)
Solve by substitution: y = x + 3, y = 2x + 5
Solution is (-2, 1)
What is Mrs. Winslow's favorite color?
Purple
Solve: 8x+y = 27 and -3x+4y = 3
What is (3,3)
When you solve a system of equations, your answer is a ...
A point, no solution, or infinite solutions
Lawn Care charges $30 per bag of mulch and a $30 delivery fee. Yard Depot charges $25 per bag of mulch and $55 for a delivery fee. At what number of bags is the cost the same?
Solution is 5 bags, $180.
Solve by substitution: x = 2y - 4, x + 8y = 16
Solution is (0, 2)
When you solve a system of equations by Elimination. How do you know if you are supposed to add the two equations? (give an example)
If the coefficient are opposites.
-3x and 3 ; -3 and 3 are opposite
Solve: 6x - 4y = 30 and 12x + 5y = -18
What is (1,-6)
What is system of linear equations ?
A set of equations that have the same unknowns.
Anthony has $7 saved up and saves $1 more each week. Marc has $4 saved up and saves $2 more each week. When will they have the same amount saved up?
Solution is 3 weeks, $10
Solve by substitution: 2x + y = -4, x = -7 - y
Solution is (3, -10)
Is (1,3) a solution of: 2x + y = 5, -2x + y = 4
Show work.
No, 2(1) + (3) = 5 but -2(1) + 3 = 1, not 4
At an office supply store, Emilio bought 3 notebooks and 5 pens for $13.75. If a notebook costs $1.25 more than a pen, how much does one notebook cost?
What is $2.50