sys eq

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

How can you solve a system of equations graphically?

Back

To solve a system of equations graphically, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, they have the same slope and will never intersect, meaning there is no solution to the system.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

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 other variable.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system has at least one solution, which can be either one unique solution or infinitely many solutions.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, typically represented by parallel lines that never intersect.