Solving Systems of Equations

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 for two equations to intersect on a graph?

Back

It means that the solution to the system of equations is the point where the two lines meet, representing the values of the variables that satisfy both equations.

Front

What is the solution to a system of equations?

Back

The values of the variables that make all equations in the system true.

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.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

By graphing the equations and observing their intersection points or by analyzing the coefficients and constants in the equations.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

If x + y = 10 and x - y = 2, what is the value of x and y?

Back

x = 6, y = 4.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.