Systems of Equations (Substitution)

Front

What is the solution (x, y) to a system of equations?

Back

The point where the equations intersect.

Front

What method is best to use when one variable is isolated in a system of equations?

Back

Substitution because a variable is isolated.

Front

How many solutions can a system of equations have?

Back

One solution, no solution, or infinite solutions.

Front

Solve the system of equations using substitution: y = 8, y = -4x + 4.

Back

(-1, 8)

Front

Solve the system of equations: y = 8x + 1, y = 6x + 3.

Back

(1, 9)

Front

What does it mean if two lines in a system of equations are parallel?

Back

They have no solution because they never intersect.

Front

What is the substitution method in solving systems of equations?

Back

Replacing one variable with an expression from another equation.

Front

If a system of equations has infinite solutions, what does that imply about the lines?

Back

The lines are coincident, meaning they lie on top of each other.

Front

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

Back

Isolate one variable in one of the equations.

Front

What does it mean for a system of equations to have one solution?

Back

The lines intersect at exactly one point.