Substitution: Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved simultaneously.

Front

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

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the substitution method?

Back

A technique for solving systems of equations by expressing one variable in terms of the other and substituting it into the second equation.

Front

What is an infinitely many solutions scenario in a system of equations?

Back

This occurs when the equations represent the same line, leading to an infinite number of intersection points.

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

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

Back

Isolate one variable in one of the equations.

Front

What does it mean if a system of equations has a unique solution?

Back

It means the lines represented by the equations intersect at exactly one point.

Front

How can you check your solution for a system of equations?

Back

Substitute the solution back into both original equations to verify that both are satisfied.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane, where intersections indicate solutions.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.