Solve Systems by 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 it mean to solve a system of equations by substitution?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

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

Back

Isolate one variable in one of the equations.

Front

Given the equations 4x - 3y = 18 and y = -2, how do you solve for x?

Back

Substitute y = -2 into the first equation: 4x - 3(-2) = 18.

Front

What is the solution to the system of equations y = -2 and 4x - 3y = 18?

Back

The solution is (3, -2).

Front

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

Back

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

Front

How can you tell if two equations have the same slope?

Back

If the coefficients of x and y in both equations are proportional, they have the same slope.

Front

What is the graphical representation of a system of equations with one solution?

Back

Two lines that intersect at a single point.

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2, 5).

Front

What does the term 'inconsistent system' refer to?

Back

A system of equations that has no solution.