Substitution systems

Front

What is a substitution system in mathematics?

Back

A substitution system is a method for solving systems of equations by expressing one variable in terms of another and substituting that expression into another equation.

Front

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

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

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

Given the equations: y = 3x and 12x - 4y = 20, what is the solution?

Back

no solutions

Front

Given the equations: y = 2x + 4 and 3x - y = 6, what is the solution?

Back

(6, 8)

Front

What is the solution to the system of equations: y = x + 3 and 2x + y = 10?

Back

(1, 4)

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the values of the solution into each equation to see if they hold true.

Front

What is the solution to the system: -7x - 2y = -13 and x = 2y + 11?

Back

(3, -4)

Front

Given the equations: x = -2y and 3x + 4y = -8, what is the solution?

Back

(-8, 4)

Front

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

Back

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