Linear Systems Substitution Method

Front

What is the solution to a system of equations?

Back

The solution is any ordered pair that makes both equations true.

Front

If a linear system has one solution, what is that solution called?

Back

An ordered pair.

Front

What is the best method for solving the system: y = 3x - 11 and 4x + 8y = 6?

Back

Substitution.

Front

How do you solve the system using the substitution method: 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2,5).

Front

What is the solution to the linear system using the substitution method: 10x + y = 14 and -8x + 3y = 23?

Back

The solution is (0.5, 9).

Front

What is the substitution method in solving linear systems?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What does it mean if a linear system has no solution?

Back

It means the lines represented by the equations are parallel and do not intersect.

Front

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

Back

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

Front

What is the first step in the substitution method?

Back

Isolate one variable in one of the equations.

Front

How can you check if your solution to a system of equations is correct?

Back

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