Systems of Equations - Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does substitution mean in the context of systems of equations?

Back

Substitution is a method for solving systems of equations where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you solve the system: -3x - 3y = 3 and y = -5x - 17?

Back

Substituting y from the second equation into the first gives: -3x - 3(-5x - 17) = 3. Solving this yields x = -4, then substituting back gives y = 3.

Front

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

Back

Substituting y = -2 into 4x - 3(-2) = 18 gives 4x + 6 = 18. Solving this yields x = 3, so the solution is (3, -2).

Front

How do you solve the system: -2x + 6y = 6 and -7x + 8y = -5?

Back

Using substitution or elimination, we find x = 3 and y = 2, so the solution is (3, 2).

Front

What is the solution to the system: 2x - 3y = -1 and y = x - 1?

Back

Substituting y = x - 1 into 2x - 3(x - 1) = -1 gives x = 4, and substituting back gives y = 3. The solution is (4, 3).

Front

How do you solve the system: -7x - 2y = -13 and x - 2y = 11?

Back

Using substitution or elimination, we find x = 3 and y = -4, so the solution is (3, -4).

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

What is the importance of finding the solution to a system of equations?

Back

Finding the solution helps determine the values of the variables that satisfy all equations simultaneously, which is crucial in real-world applications.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solution, meaning the lines represented by the equations are parallel and never intersect.