Chapter 1
Solve the equation for c.
-14 = c - 12
c = -2
Find the slope of the ordered pairs.
(0, 3) and (2, 5)
Slope = 1
When solving a system of linear equations, what does the solution represent?
The solution of a system of linear equation is the point of intersection between the equations. The point of intersection is a solution for both equation.
What is the formula for slope?
Slope = (y2-y1) / (x2-x1)
Solve the equation for d.
2d - 15 = 3
d = 9
y = -4x - 6
Slope = -4
y-intercept = -6
Solve the system of linear equations.
y = -9x + 2
y = -3x - 4
(1, -7)
Solve the equation for x.
2x + 6 = 9 (3 + x)
x = -3
Solve the equation for p.
p = -1/3
Identify the slope and y-intercept.
-6x + 3y = 12
Slope = 4
y-intercept = 2
Solve the system of linear equations.
2y = 3 + 6x
4y = 6 + 12x
Infinite solution
Solve the system of linear equations.
y = 11x + 8
y = 9x -6
(-7, -69)
The cost (in collars) of making w wedding cake is represented by C = 25w + 40. How many wedding cakes are made when the cost is $315?
11 wedding cakes
Identify the slope and y-intercept.
3x - 4y = 24
Slope = 3/4
y-intercept = -6
Solve the system of linear equations.
y = -5x -2
5x + y = 0
No solution, parallel lines
Explain how you can instantly determine whether a system of linear equations has no solution.
A system of linear equations has no solution if they have the same slope.
You rent a video game for $3.50. Your total cost of rentals for the month was $31.50. Write and solve an equation to find the number of video game rentals for the month.
3.50g = 31.50
g = 9Which is steeper, hill A that rises 2 feet for every 10 feet of run, or hill B that rises 2 feet for every 15 feet of run? Explain.
Hill A has a slope of 2/10, whereas Hill B has a slope of 2/15.
Hill A is steeper because it has a greater slope.
Solve the system of linear equations.
2x + 10y = -20
-x + 4y = 28
(-20, 2)
Explain how to solve a system of linear equation by elimination.
1. Multiply, if necessary, one or both equations by a constant so at least 1 pair of like terms has the same or opposite coefficients.
2. Add or subtract the equations to eliminate one of the variables.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value from step 3 into one the original equations and solve.