Equations with 2 Variables
What is the slope in y = 2x + 1?
2
Solve: x + 5 = 12
x = 7
What is a monomial?
A polynomial with one term
Factor: x² - 9
(x + 3)(x - 3)
What is a system of equations?
Two or more equations solved together
What is the y-intercept of y = -x + 5?
5
Solve: 2x - 4 = 10
x = 7
-x2 - 4x + 1
Factor: x² + 5x + 6
(x + 2)(x + 3)
Solve: x + y = 10, x - y = 4
x = 7, y = 3
Find x-intercept of y = 2x - 4
x = 2
Solve: 3(x - 2) = 9
x = 5
Add: (2x² + 3x) + (x² - x)
3x² + 2x
Factor: 2x² + 4x
2x(x + 2)
Name a method to solve a system.
Substitution, Elimination, Graphing
Write the equation of a line with slope 2 and y-intercept -3.
y = 2x - 3
Solve: 2x + 3 = x + 8
x = 5
Subtract: (5x² + 2x) - (2x² + x)
3x² + x
Factor completely: y3 + 64
(y + 4)(y2 - 4y + 16)
What does it mean if two lines are parallel?
No solution; they never intersect
What is the slope of a vertical line?
undefined
Solve: 2(x + 1) = 3(x - 2)
x = 8
Multiply: (x + 2)(x + 3)
x² + 5x + 6
Factor by grouping: x³ + x² + x + 1
(x² + 1)(x + 1)
Solve: 2x + y = 7, x - y = 1
x = 2, y = 3