Solving Equations
What is the first step in solving the equation: 3x+5=2x−7?
Subtract 2x from sides or add 7 on both sides. COMBINE LIKE TERMS
What do we call a system of equations that has exactly one solution?
One Solution
What does the intersection of two lines on a graph represent?
The solution to the system of equations
One company charges $10 plus $2 per mile. Another charges $5 per mile. Write equations for each.
y = 2x + 10
y = 5x
What is another name for the y-intercept?
Starting value, initial value, b in y=mx+b
Solve for x: 5x - 3 = 2x + 9
x = 4
What do we call two equations that have the same slope and different y-intercepts?
No solution -- the lines are parallel.
Graph the system
y=−2x+10 y = -2x + 10 and
y=3x−5y = 3x - 5.
How many solutions does it have?
One Solution
How do you determine when two bike rental companies charge the same price?
et their equations equal to each other and solve for x?
What is the formula for the slope?
The 'm' value in y = mx+ b
Solve for x:
-2 + 3x + 5x = 4x - 20 + 14
x = -1
What does it mean if a system of equations has infinitely many solutions?
The two equations represent the same line, so they intersect everywhere
How do you know if a system of equations has no solution just by looking at the equations?
If the slopes are the same but the y-intercepts are different, the lines are parallel and never meet
A gym charges $20 per month plus $5 per class. Another charges $10 per month plus $8 per class. When do they cost the same?
Solve
20 + 5x = 10 + 8x
Define "slope".
The rate of change, rise over run, steepness of a line
What is the LAST STEP in solving
4x + 7 = 23?
Divide by 4 on both sides
Match the definitions:
1 = Only one answer;
2 = Parallel lines never intersect;
3 = Same line; all points are solutions
Describe the steps to graph a system of equations.
Find y-intercepts, plot points, use slope to find more points, draw lines, find intersection if it exists
In a word problem, what does the point of intersection represent?
The values where both equations are equal – the break-even point
What is the slope of a horizontal line?
0 - no rise, only run
What does it mean to check your solution?
Substituting the value of x back into the original equation to verify the answer is correct
What does a system of equations look like when there is no solution?
Two parallel lines with different y-intercepts
What is the solution to the system
y = x + 3
y = -x - 1
(-2,1)
Two cell phone plans cost the same at 6 months. One charges $50 per month, the other charges $40 plus $10 per month. Write and solve an equation.
50x = 40 + 10x, solution x = 1
What are the possible numbers of solutions a system of linear equations can have?
One solution, no solution, infinitely many solutions