Systems of Equations: Substitution Method

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 of equations using substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the first step in the substitution method?

Back

Isolate one variable in one of the equations.

Front

Given the equations y = 2x + 3 and 4x - y = 1, how do you solve using substitution?

Back

Substitute y from the first equation into the second: 4x - (2x + 3) = 1.

Front

What is the solution to the system of equations: 2x + 3y = 6 and y = 2 - x?

Back

(0, 2).

Front

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

Back

Substitute the point into both equations; if both equations are true, the point is a solution.

Front

What is the solution to the system of equations: x + y = 5 and y = 3x - 1?

Back

(2, 3).

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 using substitution: y = x + 2 and 2x + y = 10.

Back

(4, 6).