Solving Systems of Equations: Substitution Method

Front

What is the substitution method in 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 does it mean for an ordered pair (x,y) to be a solution to a system of equations?

Back

It means that the ordered pair makes both equations in the system true.

Front

How do you begin graphing the equation y = 2x - 3?

Back

Start by placing a point at -3 on the y-axis.

Front

What is the first step in the substitution method?

Back

Solve one of the equations for one variable.

Front

When solving for y in the equation 2x + y = 14, what should you do to isolate y?

Back

Subtract 2x from both sides to get y = 14 - 2x.

Front

What is the importance of checking your solution in a system of equations?

Back

Checking ensures that the solution satisfies both equations, confirming its accuracy.

Front

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

Back

It means that the system of equations has one unique solution, represented by the coordinates of the intersection point.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Front

What happens if the lines of a system of equations are parallel?

Back

If the lines are parallel, the system has no solution because the equations represent lines that never intersect.

Front

What is the graphical representation of a solution to a system of equations?

Back

The solution is represented by the point where the graphs of the equations intersect.