Stojk's Holiday Systems Flashcard

Front

What is a system of equations with no solution?

Back

A system of equations with no solution is when the graphs of the equations are parallel lines, meaning they never intersect.

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

Solve the system of equations using the substitution method: 3x + 2y = 8, 4x - y = 7.

Back

x = 2, y = 1

Front

Solve the system of equations using the substitution method: 4x - 3y = 10, 2x + y = 5.

Back

x = 2.5, y = 0

Front

What does it mean to solve a system algebraically?

Back

Solving a system algebraically means finding the values of the variables that satisfy all equations in the system using algebraic methods.

Front

Solve the system algebraically: -7x - 2y = -13, x - 2y = 11.

Back

(3, -4)

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 graphs of the equations.

Front

What does it mean if the graph of a system of equations is a point?

Back

If the graph of a system of equations is a point, it means there is exactly one solution to the system.

Front

Graph the following system of equations: y = 3x - 2, y = x + 4.

Back

The graph of the system of equations is a point at (3, 7).

Front

What is the significance of the slopes of lines in a system of equations?

Back

The slopes of the lines indicate whether the system has one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).