All About Equations & Systems
Solving Systems of Linear Equations: Graphing
Solving Systems of Linear Equations: Substitution1
Solving Systems of Linear Equations: Substitution2
How Many Solutions?
100
What are the steps to graphing a line in slope-intercept form (y = mx + b)?
Be sure to state what b and m mean!
Plot b (the y-intercept) and then use m (slope) to rise and run to the next point
100
What is the solution to the system of linear equations?
(2,2)
100
What is the first step of substitution method?
Get x or y alone in one of the equations
(isolate a variable)
100
Solve the systems of equations using substitution:
y = 3x - 10 x = 2
(2,-4)
100
How many solutions does the system of linear equations have?
One! (-4,-6)
200
What are the steps to graphing a line in standard form (Ax + By = C)?
Find and plot the x-intercept using:
x = C / A
Find and plot the y-intercept using:
y = C / B
Then connect the points!
200
What is the solution?
(-1,1)
200
Is it possible to find no solutions when solving a system using substitution method?
Yes! (if your equations make parallel lines)
200
Solve the systems of equations using substitution:
y = 2x - 10 y = 4x + 8
(-9,-28)
200
How many solutions does the system of linear equations have?
y = 3x - 5
y = 3x + 7
Zero or None
300
What does it mean to "find the solution" to a system of linear equations?
It means to find the point of intersection
300
Graph the following system and circle the solution:
y = 3x + 2
y = -1/3x + 1
Host will judge graphs
300
What is your new (one) equation after performing substitution?
y = 2x 3x + y = 20
3x+(2x)=20 or
5x=20
300
Solve the systems of equations using substitution:
y = -2x - 9 3x - 6y = 9
(-3, -3)
300
How many solutions does the system of linear equations have?
y = (-5/3)x + 3
y = (1/3)x - 3
One
400
What are all the possible number of solutions/intersections in a system of linear equations?
(there are three answers!)
Zero, One, or Infinite
400
Solve the systems of linear equations by graphing:
400
How would you isolate x in this equation?
6y + x = 20
subtract 6y from both sides to get:
x = 20 - 6y
400
Solve the systems of equations using substitution:
2x - y = 6 x = y + 5
(1, -4)
400
How many solutions does the system of linear equations have?
y = 3x + 9
2y = 6x + 18
*Hint* we need both equations to be in y = mx + b form to compare their slopes!
Infinitely many solutions
500
What are the names of the four types of systems we could graph?
Parallel, Perpendicular, Intersecting, and Same
500
Solve this by graphing:
2x - y = 4
x + 3y = 3
(3,2)
500
How would you isolate y in this equation?
4x + 2y = 20
Subtract 4x first, then divide everything by 2:
2y = -4x + 20
then,
y = -2x +10
500
Solve the system of equations using substitution:
8x − 10y = 36 6x + y = 2
(2,-10)
500
How many solutions does the system of linear equations have?
y = 2x - 5
4y = 8x - 5
*Hint* we need both equations to be in y = mx + b form to compare their slopes!
Zero or None