Systems of Equations Graphing

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 on a graph.

Front

What does it mean to solve a system of equations by substitution?

Back

Solving by substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

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

Back

(-9, -3)

Front

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

Back

(3, -4)

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 y = 6x - 11 and -2x - 3y = -7?

Back

(2, 1)

Front

What does it mean for two lines to intersect on a graph?

Back

When two lines intersect, it means they have a common solution, which is the point where they meet on the graph.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) to the system.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves isolating one variable in one equation and substituting that expression into the other equation.

Front

What is the significance of the point (1, -1) in a system of equations?

Back

The point (1, -1) is a solution to a system of equations, meaning it satisfies all equations in the system.