Systems of Equations 5.1- 5.5 Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

How do you graph the inequality y ≥ -3?

Back

Graph the line y = -3 as a solid line and shade the area above the line.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

It involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

Solve the system: x + y = 4 and -5x - 6y = -18.

Back

(6, -2)

Front

Solve the system: 2w - 3z = -1 and 3w + 4z = 24.

Back

(4, 3)

Front

What is the graphical representation of the equation 3x + y = 2?

Back

A straight line that intersects the y-axis at 2 and the x-axis at 2/3.

Front

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

Back

They determine the slope and position of the lines represented by the equations.