Solving Systems with Substitution

Front

What does it mean when a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and there are countless points (x, y) that satisfy both equations.

Front

What is the solution to the system of equations: 2x + 3y = 12 and x - y = 1?

Back

(3, 2)

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

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

Back

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

Front

What is the solution to the system of equations: 3x + 4y = 10 and 6x + 8y = 20?

Back

Infinite solutions.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

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

Back

(3, 2)

Front

What does it mean when two equations are dependent?

Back

It means they represent the same line and have infinite solutions.

Front

What is the solution to the system of equations: 2x + 5y = 10 and 4x + 10y = 20?

Back

Infinite solutions.