Solving Linear Eqs
Solve.
x - 6 = -5
x = 1
What's a simple description of a line that only ever can be found entirely in both Quadrants II and III?
A vertical line.
It costs $4 for jumbo hamburgers ("h") and $3 for sodas ("s"). I have $12 to spend and I want to spend it all. What would the linear equation be in STANDARD FORM that models this situation?
$4h + $3s = $12
Solve.
2x + 1 > 7
x > 3
What are the names of the three fundamental methods that are used to solve a system of linear equations?
Graphing, substitution, and linear combination (or elimination).
Solve.
2x + 4 = 2(x + 3)
x = no solution
What do you know about the relationship between the slopes of two lines that are perpendicular to each other?
The product of the slopes of the two lines is -1 (or, the slopes of the two lines are negative reciprocals of each other).
If the slope of a line and the y-intercept have the same value of 5, what is the equation of this line in slope-intercept form (using the variables x and y)?
y = 5x + 5
Solve. Your final solution should be a compound inequality that does NOT have an absolute value sign in it.
|x| - 1 < 3
-4 < x < 4
What is the solution to this system of equations:
x + y = 8
x - y = 4
(6,2)
Solve.
3x - x = 5 + 6 - 11
x = 0
What do "m" and "b" represent in the linear equation: y = mx + b?
m = slope
b = y-intercept
If the slope of a line is 1/3 and the line goes through the origin, what is the equation of this line in any form (using the variables x and y)?
Slope-Intercept: y = (1/3) x
Standard: x - 3y = 0
Point-Slope: y - 0 = 1/3(x - 0)
Solve. Your final solution should NOT have an absolute value sign in it.
|x| > -1
x = any (real) number
What is the solution to this system of equations:
2x - y = 3
6x - 3y = 12
There is no solution!
Solve.
3x + 8 - 2 = 3(x + 2)
x = any real number
Does the linear equation, y = 3x - 4, go through the point: (5, 11)?
Yes, because 11 = 3(5) - 4.
What would the equation of the line be that is perpendicular to the line y = -(1/2)x - 7, that has the same y-intercept as this line? Use any form and use the variables x and y.
Slope-Intercept: y = 2x - 7
Standard: 2x - y = 7
Point-Slope: y + 7 = 2(x - 0)
Solve.
|x - 7| = 7
x = 14, 0
What is the solution to this system of equations:
3x - 4y = -9
12x - 16y = -36
There are infinitely many solutions!
Solve.
3(x + 4) = 2x + 3 + 7
x = -2
What are the x- and y-intercept of the line:
y = 6x - 2?
x-intercept = 1/3
y-intercept = -2
What is the equation of the line that goes through the points (5,5) and (7,7)? Use any form and use the variables x and y.
Slope-Intercept: y = x
Standard Form: x - y = 0
Point-Slope: y - 0 = 1(x - 0)
Solve.
|x| = |-x|
x = any (real) number
What is the solution to this system of equations:
x + 5y = 10
4x + 24y = 48
(0,2)