7.2 Ordered Pair Solutions to Systems of Equations

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a two-dimensional space, written in the form (x, y), where 'x' is the horizontal coordinate and 'y' is the vertical coordinate.

Tags

CCSS.5.G.A.1

Front

What does it mean for an ordered pair to be a solution to a system of equations?

Back

An ordered pair is a solution to a system of equations if it satisfies all equations in the system, meaning that when the values of 'x' and 'y' are substituted into the equations, both equations hold true.

Front

How do you determine if an ordered pair is a solution to a system of equations?

Back

To determine if an ordered pair is a solution, substitute the 'x' and 'y' values into each equation of the system. If both equations are true, then the ordered pair is a solution.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system of equations, indicating the values of 'x' and 'y' that satisfy both equations simultaneously.

Tags

CCSS.8.EE.C.8B

Front

What is the graphical representation of a system of equations?

Back

A system of equations can be represented graphically by plotting each equation on the same coordinate plane. The points where the graphs intersect represent the solutions to the system.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines in a system of equations are parallel?

Back

If two lines in a system of equations are parallel, it means they have the same slope but different y-intercepts, indicating that there is no solution to the system as they never intersect.

Tags

CCSS.8.EE.C.8B

Front

What does it mean if two lines in a system of equations coincide?

Back

If two lines in a system of equations coincide, it means they are the same line, indicating that there are infinitely many solutions to the system.

Tags

CCSS.8.EE.C.8A

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you verify if a point is a solution to a linear equation?

Back

To verify if a point is a solution to a linear equation, substitute the x-value into the equation and check if the resulting y-value matches the y-value of the point.

Front

What is the role of substitution in solving systems of equations?

Back

Substitution involves solving one equation for one variable and then substituting that expression into the other equation to find the values of the variables.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6