Graphing
How do you graph a linear equation?
Plot two points and draw a straight line passing through them.
What is the first step in solving a system of equations using the substitution method?
Solve one of the equations for one variable in terms of the other variable.
What is the purpose of the elimination method in solving systems of linear equations?
The elimination method is used to eliminate one variable by adding or subtracting the equations.
If the graph of two linear equations is parallel, do they have a solution?
No, parallel lines do not intersect, so there is no solution.
Solve the system of linear equations using the substitution method:
The solution is x = 2, y = 3.
Solve the system of linear equations using the elimination method:
The solution is x = 2, y = 1.
How can you determine the solution to a system of linear equations by graphing?
The solution is the point(s) where the graphs of the equations intersect.
Can the substitution method be used to solve any system of linear equations?
Yes, the substitution method can be used for any system of linear equations.
The elimination method always requires multiplying one or both equations by a negative number.
False- some might be already set up
Solve the system of linear equations by graphing:
The solution is (1, 5).
Solve the system of linear equations using the substitution method:
The solution is x = 1, y = 5.
Solve the system of linear equations using elimination
Equation 1: −4x − 2y = −12
Equation 2: 4x + 8y = −24
Answer: (6,-6)
True or False: The system of linear equations has infinitely many solutions if the graphs of the equations coincide.
True.
Can you explain how the substitution method works in solving systems of linear equations?
The substitution method involves solving one equation for one variable and then substituting that expression into the other equation to find the value of the other variable.
Solve the system of linear equations using the elimination
Equation 1: 2x + 8y = 6
Equation 2: −5x − 20y = −15
infinite # of solutions