Midterm Practice #1 ORCA 1

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. Solutions are the points where the equations intersect.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

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

Front

How do you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the slope-intercept form of a line?

Back

The equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the slope from an equation in slope-intercept form?

Back

The slope is the coefficient of x in the equation y = mx + b.

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, represented by the value of b in y = mx + b.

Front

How do you solve a system of equations using substitution?

Back

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

Front

What is a determinant in a matrix?

Back

A scalar value that can be computed from the elements of a square matrix, indicating whether the matrix is invertible.

Front

How do you evaluate the determinant of a 2x2 matrix?

Back

For a matrix [[a, b], [c, d]], the determinant is ad - bc.