Vocab
A ___________________________________ is a set of two or more linear equations in the same variables. An example is shown below:
y=x+1
y=2x-7
System of Linear Equations
Is the following slope intercept form:
y = 2x + 3
yes
Solve the system:
y=x+1
y=−x+3
Answer (1,2)
A _____________________________________ in two variables is an ordered pair that is a solution of each equation in the system. The solution of a system of linear equations is the point of intersection of the graphs of the equations. (The point that the lines cross)
solution of a system of linear equations
Rewrite x + y=6 in slope-intercept form
y = -x + 6
Solve the system:
y=−2x+4
y=x−2
Answer: (2,0)
A line that goes up or down at a constant rate
What is a linear equation?
Write your own equation that is in slope intercept form
y = mx + b
Solve the system:
y=3x+2
y=3x−4
No solution — the lines are parallel.
Draw a graph AND explain your answer:
How many solutions are there to a system of two lines that intersect once have?
One solution
Rewrite 2x−y=4 in slope-intercept form.
y = 2x - 4
Solve the system:
y=x−2
y=−x+4
Answer: (3,1)
Draw a graph AND explain your answer:
How many solutions are there to a system of two lines that do not intersect?
no solution
Rewrite 4x+5y=20 in slope intercept form
y=−(4/5)x + 4
y=2x+3
4x−2y=−6
Infinitely many solutions