Solve System by Substitution

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system by substitution?

Back

To solve one equation for one variable and 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

If y = 2x + 3, what is y when x = 4?

Back

y = 2(4) + 3 = 11.

Front

What is the solution to the system: y = x + 2 and y = 3x - 4?

Back

(2, 4).

Front

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

Back

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

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

Solve the system: y = 3x + 1 and y = -x + 5. What is the solution?

Back

(1, 4).

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions to the system.