Systems of Equations (Substitution)

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is substitution in the context of systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

How can you determine the number of solutions in a system of equations?

Back

By analyzing the graphs of the equations: one solution (intersecting lines), no solution (parallel lines), or infinite solutions (same line).

Front

What is the solution to the system of equations y = 2x + 3 and y = -x + 1?

Back

(1, 5)

Front

If y = 4x + 2 and y = 2x + 6, how many solutions does this system have?

Back

No solution (the lines are parallel).

Front

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

Back

Solve one of the equations for one variable in terms of the other.

Front

Solve the system: y = 2x + 1 and 3y - x = 7.

Back

(2, 5)

Front

What does it mean if two equations represent the same line?

Back

They have infinite solutions because every point on the line is a solution.

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.