Algebra 1 Unit 5 Flashcards
What is a system of equations?
Two or more equations with the same variables
What is the solution, graphically, to a system?
The point (x,y) where the two lines intersect
What is the solution, algebraically, to a system?
The point (x,y) that makes bothe equations true
What are the three types of solutions a system can have?
Intersecting lines, parallel lines, and the same line
How many solutions do intersecting line have?
It has one solution written as a point (x,y)
How many solutions do parallel lines have?
They have no solution written as a circle with a line through it
How many solutions do two same lines have?
They have infinitely many written as a sideways 8
What are the three steps to solve a system by graphing?
- Rewrite the equations in slope intercept form
- Graph the Lines
- Identify the solution(s)
If a system of linear equations has one solution, what does this mean about the two lines?
The lines intersect
If a system of linear equations has no solution, what does this mean about the two lines?
The lines are parallel
If a system of linear equations has infinately many solutions, what does this mean about the two lines?
The lines are the same
What is the substitution method of solving systems?
It substitutes one equation within the other
What is the first step when solving a system by substitution?
Solve one equation for x or y
When should you use substitution?
When you can isolate a variable with no coefficient
What is the elimination method of solving equations?
It adds or subtracts two equations to eliminate a variable
What is the first step when solving a system by elimination?
Line the equations up for all parts
What if eliminatin systems have no common coeficients?
Multipy one or both equations by some number to create matching/opposite coefficients
What is a linear inequality?
Similar to a linear equation, but uses an inequality symbol
What is a possible solution to a linear inequality?
Any of the oredered pairs that make the inequality true
Is (2,5) a solution of 2x - 3y < 15?
Yes! -11< 15
Is (-1, -7) a solution of 2x - 3y < 15?
No! 19 < 15
Is (3, -4) a solution of 2x - 3y < 15?
No! 18 < 15
Is (0,0) a solution of 2x - 3y < 15?
Yes! 0 < 15
What is the best test point when shading a graphed inequality?
The origin (0,0)
A greater symbol means shade __________.
Above, make sure y is on the left side of the inequality though
A less symbol means shade __________.
Below, make sure y is on the left side of the inequality though
Graph a solid line when the inequality sign is ________.
Equal to
Graph a dotted line when the inequality sign is ________.
Only greater or less than
What would create a sign to flip/change directions?
When you multiply or divide by a negatove value
What is a systems of linear inequalities?
Two or more linear inequalities that are graphed together
What is the solution to a system of linear inequalities?
The solution is the overlapping region of points that satisfies both inequalities
