Systems 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 systems of equations?

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 the system: y = -3x + 5 and 5x - 4y = -3?

Back

Substituting y from the first equation into the second gives x = 1, then y = 2.

Front

What is the solution to the system: -3x - 8y = 20 and -5x + y = 19?

Back

The solution is (-4, -1).

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

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

Back

It means the lines are parallel and never intersect.

Front

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

Back

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

Front

How do you check the solution of a system of equations?

Back

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

Front

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

Back

Isolate one variable in one of the equations.

Front

What is the solution to the system: -2x + 6y = 6 and -7x + 8y = -5?

Back

The solution is (3, 2).