Systems of Equations by Graphing Point of Intersection

What is the solution to the system?

• No solution

• (0, 2)

• (0, -4)

• (3, -3)

Identify which method for solving systems is being described by this fact: Equations must be written in slope-intercept form

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact: When the lines are parallel and do not intersect at any points the solution is No Solutions.

• Graphing

• Substitution

• Elimination (adding or multiplying)

• All 3 methods

Identify which method for solving systems is being described by this fact: When the lines are intersecting at every point because they coincide and are the exact same line the solution is Infinite Solutions.

• Graphing

• Substitution

• Elimination (adding or multiplying)

• All 3 methods

Identify which method for solving systems is being described by this fact:
The drawback to using this method is that integer values are not always found at the intersection point and the solution might need to be estimated.

• Graphing

• Substitution

• Elimination (adding or multiplying)

• All 3 methods

Let's solve a system by GRAPHING. Put the steps in order from first to last.

• Solve both equations for y to get slope-intercept form

• Graph both lines using the slope and y-intercept

• The intersection point is the solution

Graph both equations on the same coordinate plane.

y=4x-3

y=-3x+4

How can you determine if a system of equations has one solution by graphing?

• The lines are perpendicular

• The lines are parallel

• The lines intersect at one point.

• The lines do not intersect

If the lines representing a system of equations intersect at the point (3, 4), what is the solution of the system?

• (1, 1)

• (3, 4)

• (5, 2)

• (0, 0)

How can you identify the point of intersection of two lines when graphing a system of equations?

• Find the coordinates where the two lines intersect on the graph.

• Calculate the average of the two lines

• Draw a circle around the point of intersection

• Count the number of points on each line