Systems of Equations/ Word Problems

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 for a system of equations to have no solution?

Back

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

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

A system of equations has infinitely many solutions when the equations represent the same line, meaning they overlap completely.

Front

How do you solve a system of equations using substitution?

Back

To solve by substitution, solve one equation for one variable, then substitute that expression into the other equation.

Front

How do you solve a system of equations using elimination?

Back

To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the other.

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).

Front

What does the solution (4, 2) represent in a system of equations?

Back

The solution (4, 2) represents the values of the variables that satisfy both equations in the system.

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.

Front

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

Back

Substitute the solution values into both equations. If both equations are true, the solution is correct.

Front

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

Back

Substitute y from the first equation into the second equation to solve for x.