Graphing systems of equations
What is the point where two lines cross called?
The intersection point.
What do you do first in substitution?
Solve one equation for a variable
What is the goal of elimination?
To eliminate one variable
Why do we multiply equations in elimination?
To create opposite coefficients
What line style is used for < or > inequalities?
(Hint) type of line
Dashed line
Y=x+1
Y=-x+5
2,3
Solve using substitution:
y=x+2
x+y=8
(3,5)
Solve:
x+y=10
x−y=4
(7,3)
Solve:
x+y=7
2x−y=5
(4,3)
Should you shade above or below the line for y>x+2?
Above the line
True or false: Parallel lines have no solution
True
Solve using substitution:
y=2x+1
x+y=10
(3,7)
Solve:
2x+y=9
2x−y=1
(2.5,4)
Solve:
3x+2y=12
x−2y=4
(4,0)
What does the overlapping shaded region represent?
The solutions to both inequalities
What does it mean if two equations graph as the same line?
Infinitely many solutions
If substitution gives you a answer like 4=4, what does that mean?
(Hint) how many solutions
Infinitely many solutions
Why do opposite coefficients help in elimination?
They cancel out a variable
Solve:
2x+3y=13
4x−3y=11
(4,1.67)
Is the line solid or dashed for y≤3x−1?
Solid line
Solve by graphing:
y=2x−3
y=−x+6
(3,3)
Solve using substitution:
y=3x−2
2x+y=13
(3,7)
Solve:
3x+y=13
3x−y=5
(3,4)
Solve:
5x+2y=18
3x−2y=2
(2,4)
Graph and identify the solution region:
y>x−2
y≤−x+6
The overlapping region above y=x−2 and below or on y=−x+6