System of Equations Substitution

Front

What is a system of equations?

Back

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

Front

What does substitution mean in the context of solving equations?

Back

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

Front

Solve the system by substitution: y = 2x + 3, x + y = 10.

Back

(2, 6)

Front

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

Back

Identify one equation to solve for one variable in terms of the other variable.

Front

Solve: y = 3x + 4, 2y - x = 10.

Back

(2, 10)

Front

What is the graphical representation of a system of equations?

Back

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

Front

Solve: y = -x + 1, y = 2x - 3.

Back

(-2, 3)

Front

What does it mean if a system of equations has no solution?

Back

It means the lines are parallel and never intersect.

Front

Solve: y = 5x - 2, 3y + 2x = 16.

Back

(4, 18)

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, and every point on the line is a solution.