Flashcard: Solve Linear Systems Using Substitution

Front

What is a linear system of equations?

Back

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

Front

What does substitution mean in solving linear systems?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the first variable.

Front

Back

(2, -2)

Front

Back

Front

Back

(3, 15)

Front

Back

Front

Back

@@igg(rac{2}{3},-rac{13}{3}igg)@

Front

What is the graphical representation of a linear system?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

What does it mean if a linear system has no solution?

Back

It means the lines are parallel and never intersect, indicating that there are no values for the variables that satisfy both equations.