Explore of Linear Equations

When the line graphs of a linear system intersect, that point is the solution of the system. However, sometimes the line graphs of a system do not intersect. There are two situations when this is true. First, if the lines are parallel, they will not intersect. In this situation, there is no solution. Second, one line lies on top of the other line. Therefore, the lines are always touching. In this situation, there are infinitely many solutions.

• A system of equations, whose graphs are parallel lines, has no solution.

• A system of equations, whose graphs appears to be one line, has infinitely many solutions.

• A system of equations, whose graphs intersect, has one and only one solution.

• A system of equations will have one of three possible solutions (1) exactly one, (2) no solution, or (3) infinitely many solutions.

Tags

CCSS.8.EE.C.8B

The solution of a system of equations is the solution that both equations share. That is, it is the point where the graphs of the equations intersect.

What is the solution of this system of equations?

• (0, 6)

• (0, -4)

• (2, 2)

• (-2, - 2)

Tags

CCSS.8.EE.C.8B

A system of equations may be solved by graphing or algebraically. If solved by graphing, observe the graph to determine the solution: (1) if the lines intersect, the point of intersection is the solution, (2) if the lines are parallel, there is no solution, and (3) if there appears to be only one line, there are infinitely many solutions. If you solve algebraically, the values of x and y will determine the solution: (1) if a value is found for x and y, those values are written as an ordered pair, which is the solution, (2) if the x and y values are eliminated and the result is a false statement (such as 3 = 0), there is no solution, and (3) if the x and y values are eliminated and the result is a true statement (such as 3 = 3), there are infinitely many solutions. Select all true statements pertaining to solving a system algebraically.

• When solving, if the final answer produces a value for x and y, this system has one solution.

• When solving, if the final answer produces a false statement, this system has no solution.

• When solving, if the final answer produces a true statement, this system has infinitely many solutions.

• When solving, if the final answer produces a fraction, you have made a mistake.

Tags

CCSS.8.EE.C.8B

• Eliminate the x-value by addition

• Eliminate the y-value by addition

• Eliminate the y-value by multiplication

• Eliminate the x-value by subtraction

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• (6, 0)

• (4, 6)

• (6, 4)

• (0, 6)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• (5, 7)

• (7, 2)

• (7, 5)

• (5, 3)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

• (2, -1)

• (-2, 2)

• (1, -2)

• (-2, 1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What is the solution to this system of equations?

• (6, 1)

• (-1, 6)

• (6, -1)

• (1, 6)

Tags

CCSS.8.EE.C.8B

Write an equation of a line in slope-intercept form with the given slope and y-intercept. Slope: 3, y-intercept: 5

• y=3x+5

• y=-2x-9

• y=2/3x+3

• y=-5/8x-2

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

• A
• B
• C
• D