Systems of equations substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is substitution in the context of solving equations?

Back

Replacing one variable with an expression involving another variable.

Front

How do you solve the system of equations: y = 8 and y = -4x + 4?

Back

Substituting y = 8 into the second equation gives -4x + 4 = 8, leading to x = -1. The solution is (-1, 8).

Front

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

Back

Substituting x = 6 into the second equation gives y = 2(6) - 3 = 9. The solution is (6, 9).

Front

What does it mean if two lines intersect on a graph?

Back

It means there is a unique solution to the system of equations represented by those lines.

Front

What is an infinite solution in a system of equations?

Back

When the equations represent the same line, resulting in countless points of intersection.

Front

What is a no solution scenario in a system of equations?

Back

When the equations represent parallel lines that never intersect.

Front

How can you identify a system of equations with infinite solutions?

Back

Both equations can be rewritten to show they are equivalent, such as 2x + 4y = 8 and x + 2y = 4.

Front

What is the graphical representation of a system of equations?

Back

The lines or curves representing each equation plotted on a coordinate plane.