Solving Systems of an Equation

x = x

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

0 = 0

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

An ordered pair in a system that makes all equations true is

• consistent system

• system of linear equations

• solution of a system to linear equations

• independent system

Which point satisfies both equations?

y - x = 2

y + 2x = 2

• (0, 2)

• (2, 0)

• (2, 4)

• (-2, 6)

At which point do the graphs of these equations intersect?

4x + 3y = 12

2x - 5y = -20

• (0, 4)

• (4, 0)

• The graphs do not intersect.

• The graphs represent the same line

Which ordered pair represents the solution to the equations shown in the graph?

• (0, 6)

• (6, 0)

• (0, 10)

• (10, 0)

This is a system of equations.

-2x + y = -8

-x + 2y = -4

How many solutions are there for this system of equations?

• 0

• 1

• 2

• an infinite number

The first equation in a system of two equations is x + 4y = 8. If the graph of the second equation does not intersect the graph of the first equation, what could be a second equation for this system?

(HINT: Convert the first equation to slope-intercept form.)

• y = 4x + 1

• y = 1/4x - 2

• y = -4x + 3

• y = -1/4x - 5

Jessica is solving the system of equations shown below.

y = 3x + 2

y = 2x + 7

If she graphs this system on a coordinate plane, how could she interpret the solution of this system?

• The system will be parallel.

• The system will be one line.

• The system will intersect at one point.

• The system will intersect at two different points.

A jar contains only nickels and quarters. The total number of coins in the jar is 15. The total value of the coins is $2.35. Which system of equations represents this situation?

• n + q = 2.35

  .05n + .25q = 15

• n + q = 15

  .5n + .25q = 15

• n + q =15

  .05n + .25q = 2.35

• .05n + q = 15

  n + .25q = 2.35