Unit 2A Solving Systems of Equations

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

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

Back

An ordered pair is a pair of numbers (x, y) that represent the coordinates of a point on a graph, where 'x' is the horizontal value and 'y' is the vertical value.

Front

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

Back

Substitute the values of the ordered pair into each equation. If both equations are true, then the ordered pair is a solution.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection of the lines representing each equation on a coordinate plane.

Front

What does it mean if two lines intersect at a point?

Back

If two lines intersect at a point, it means that there is a unique solution to the system of equations represented by those lines.

Front

What does it mean if two lines are parallel?

Back

If two lines are parallel, it means they have no points of intersection and therefore no solution to the system of equations.

Front

What does it mean if two lines coincide?

Back

If two lines coincide, it means they lie on top of each other, representing infinitely many solutions to the system of equations.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is a solid line in graphing systems of equations?

Back

A solid line indicates that the points on the line are included in the solution set, meaning the equations are equal at those points.