Solving Systems Using Graphing and Substitution

Front

What is the solution to a system of equations?

Back

The solution (x, y) to a system of equations is the point where the equations intersect.

Front

How do you find the y-value when given an equation and an x-value?

Back

Substitute the x-value into the equation to solve for y.

Front

Is (9, 9) a solution to the system of equations x + y = 18 and x - y = 0?

Back

Yes, it is a solution to the system of equations.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection point(s) of the lines representing the equations.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into each equation; if it satisfies both, it is a solution.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

Parallel lines have no points of intersection, meaning there is no solution to the system.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the graphical method for solving systems of equations?

Back

The graphical method involves plotting the equations on a graph and identifying the intersection point.

Front

What is the significance of the intersection point in a system of equations?

Back

The intersection point represents the values of x and y that satisfy both equations.

Front

How can you verify the solution of a system of equations?

Back

By substituting the solution back into the original equations to check if both are satisfied.