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 set of values that satisfy all equations simultaneously.

Front

What does it mean to solve a system of equations graphically?

Back

Solving a system of equations graphically involves plotting the equations on a graph and identifying the point(s) where the lines intersect, which represent the solution(s).

Front

What is the substitution method for 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 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 remaining variable.

Front

What is the solution to the system of equations: 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, which means they never intersect.

Front

How do you determine 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 overlap completely.

Front

What is the graphical representation of the equation y = -x + 5?

Back

This equation represents a line with a slope of -1 and a y-intercept of 5.

Front

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

Back

(1, -1)

Front

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

Back

Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.