SoE Substitution Practice

Front

What is a solution to a system of equations?

Back

A solution is a set of (x,y) coordinates that satisfy both equations in the system.

Front

How can you determine if a point is a solution to a system of equations?

Back

By checking if the (x,y) coordinates satisfy both equations.

Front

What does it mean to solve a system of equations by substitution?

Back

It means to solve one equation for one variable and then substitute that expression into the other equation.

Front

What is the first step in solving a system of equations by substitution?

Back

Isolate one variable in one of the equations.

Front

What do parallel lines indicate about their slopes?

Back

Parallel lines have the same slope.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

If two lines have different slopes, what can be said about their intersection?

Back

They will intersect at exactly one point.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

(1, 3) is the solution.

Front

What does it mean if two lines are coincident?

Back

They lie on top of each other and have infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

It is the intersection points of the lines represented by the equations.