Systems of equations substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does substitution mean in the context of solving equations?

Back

Substitution is the process of replacing a variable in one equation with an expression from another equation.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the first variable.

Front

What is the solution to the system of equations x = 6 and y = 2x - 3?

Back

(6, 9)

Front

What is the solution to the system of equations 2y + x = -15 and x = 3y?

Back

(-9, -3)

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 solution to the system of equations y = 8 and y = -4x + 4?

Back

(-1, 8)

Front

What is the solution to the system of equations 3x + 2y = 12 and y = 4 - 1.5x?

Back

(4, 0)

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.