4-1 Solving Equations by Graphing
How can you tell graphically how many solutions a system of linear equations have?
Where the two lines intersect
How do you use substitution?
Isolate the x or the y variable for one of the equations and replace it's equivalent expression into the second equation.
What is the first step in using the elimination method?
Eliminate one of the variables.
In which direction would you shade given the following inequality?
y > 2x - 1
Above the boundary line
How can you tell graphically where the solutions lie for a system of linear inequalities in two variables?
The double shaded region.
What is the solution of the system of equations when two lines are graphed and there is only one line showing on the graph?
When you use substitution and get a false statement at the end, what does that mean?
Lines are parallel, no solution.
When you use elimination and get a true statement at the end, what does that mean?
Same line, infinitely many solutions.
For a less than or equal to OR a greater than or equal to symbol, describe the line.
Solid line on the boundary line.
What is the solution of the system of equations when two lines are graphed and the lines are parallel?
No solution
When you use substitution and get a true statement at the end, what does that mean?
Same line, infinitely many solutions.
When you use elimination and get a statement such as
5 = -5
what is the solution?No solution.
Describe the graph of the inequality
Y > = 5x - 1
Solid line, shaded above the boundary line
Is (0,7) part of the solution?
y> 2x + 1
and
Y <-3x + 7
No, it is on the dotted line for y < -3x + 7
What is the solution to this system of linear equations. Use desmos to graph
Y = 2x + 1
Y = 3x
(1,3)
Use substitution to find the solution;
y = 4
3y - 2x = 18
(-3,4)
Which variable would you eliminate given this system of linear equations, and why;
3x - 2y = 9
-3x - 5y = 11
The x's because the coefficients are inverse and you can add them immediately and eliminate them.
Describe the graph of x > 1
Dashed line, shaded to the right of x = 1
What is the solution to this system of linear equations. Use desmos to graph
Y = 2x + 1
-4x + 2Y = 2
Infinitely many solutions
Use substitution to find the solution;
-3x + 6y = - 1
x = 2y + 1
No Solution
How would you manipulate the second equation to eliminate the y variables? And what would the new equation look like?
4x + 9y = -1
2x + 3y = 5
Multiply it by a -3
-6x - 9y = -15
Describe the graph of y < -4
Dashed line, shaded below y = -4
Is (-2,2) part of the solution set for the system of inequalities; (use desmos)
Y <-2/3 x + 2 and
Y > - x - 3
Yes, it is in the shaded region.