M3/Trig. Ch. 7 Systems of Equations

Front

What is a consistent system of equations?

Back

A consistent system of equations is one that has at least one solution. This can be either a unique solution (two intersecting lines) or infinitely many solutions (two coincident lines).

Front

What is the graphical representation of a consistent system with a unique solution?

Back

Two intersecting lines.

Front

What is the graphical representation of an inconsistent system of equations?

Back

Two parallel lines.

Front

What is the value of the y-coordinate of the solution to the system of equations x - 2y = 1 and x + 4y = 7?

Back

1.

Front

What is Cramer's Rule?

Back

Cramer's Rule is a mathematical theorem used to solve systems of linear equations with as many equations as unknowns, using determinants.

Front

How do you find the x-coordinate using Cramer's Rule?

Back

Replace the x-column in the coefficient matrix with the constants column, calculate the determinant of this new matrix, and divide by the determinant of the original coefficient matrix.

Front

How do you find the y-coordinate using Cramer's Rule?

Back

Replace the y-column in the coefficient matrix with the constants column, calculate the determinant of this new matrix, and divide by the determinant of the original coefficient matrix.

Front

What is the solution to the system of equations 2x - y = 4 and y = -2x + 8?

Back

x = 3.

Front

What does it mean if two lines are coincident?

Back

It means they lie on top of each other and have infinitely many solutions.

Front

What is the first step in solving a system of equations graphically?

Back

Graph each equation on the same coordinate plane.