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

What does it mean to solve a system of equations?

Back

To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection point(s) of the lines represented by the equations on a coordinate plane.

Front

What is the substitution method in solving systems of equations?

Back

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

Front

What is the elimination method in 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 variable.

Front

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

Back

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

Front

Solve the system: 5x + 3y = 6 and x - 3y = 12.

Back

(3, -3)

Front

Solve the system: 3x + y = 4 and x + 2y = -2.

Back

(2, -2)

Front

Solve for x and y: 3x + 2y = 16 and 7x + y = 19.

Back

(2, 5)