Writing and Solving Systems of Equations

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

How do you solve a system of equations graphically?

Back

To solve graphically, plot each equation on the same graph and identify the point(s) where they intersect.

Front

What is the substitution method for 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 elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the lines represented by the equations are parallel and never intersect.

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

Front

How can you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and set them equal to each other.

Front

What is the first step in solving the system: y = 4x + 1 and 3x + 2y = 13?

Back

Substitute the expression for y from the first equation into the second equation.

Front

What is the solution to the system of equations: y = 4x + 1 and 3x + 2y = 13?

Back

The solution is (1, 5).

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both original equations to see if they hold true.