Systems of Equations: Substitution Method

Front

What is a system of equations?

Back

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

Front

What does it mean for two equations to intersect on a graph?

Back

It means they have a common solution (x, y) that satisfies both equations.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the x and y values of the point into both equations; if both are true, it is a solution.

Front

What is the first step in using the substitution method?

Back

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

Front

If you have the equations y = 2x + 3 and y = -x + 1, how do you find the intersection?

Back

Set 2x + 3 = -x + 1 and solve for x.

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

Solve by substitution: x = 4y + 1, 2x - y = 3. What is the solution?

Back

(1, 0)