1/5/24 - System of Equations (substitution)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Front

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

Back

(3, 8)

Front

Solve the system: y = 8x + 1 and y = 6x + 3. What is the solution?

Back

(1, 9)

Front

Solve the system: y = 7x + 9 and 2y + 2x = -30. What is the solution?

Back

(-3, -12)

Front

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

Back

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

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

If a system of equations has no solution, what does that indicate about the lines represented by the equations?

Back

It indicates that the lines are parallel and will never intersect.

Front

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

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 solution back into both original equations to see if they hold true.