Systems of Equations and Graphs Flashcard

Front

Solve the following system by setting the two equations equal to each other: -1/3x + 4 = 2/3x + 1. What is the solution?

Back

(3, 3)

Front

What is the y-intercept of the equation y = -2/3x + 3?

Back

3

Front

Using substitution, what is the solution to the system of equations 9x - y = 17 and 5x + 4y = -27?

Back

(1, -8)

Front

Solve the system of equations: 3x - 7y = -18 and 4x - 2y = -24.

Back

(-6, 0)

Front

What is the solution to the system? (Provide the answer in the form (x, y))

Back

(6, 8)

Front

Define a system of equations.

Back

A set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines represent the solutions to the system.

Front

Explain the substitution method for solving systems of equations.

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the significance of the y-intercept in a linear equation?

Back

It is the point where the line crosses the y-axis, indicating the value of y when x = 0.