PSAT questions-Systems of Linear Equations1

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the graphs of the equations intersect.

Front

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

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

Front

What is the solution to a system of linear equations?

Back

The solution to a system of linear equations is the point (x, y) that satisfies all equations in the system.

Front

How can you determine the number of solutions in a system of linear equations?

Back

You can determine the number of solutions by analyzing the slopes and y-intercepts of the lines: 1) If slopes are different, one solution; 2) If slopes are the same and y-intercepts are different, no solution; 3) If slopes and y-intercepts are the same, infinitely many solutions.

Front

What is the graphical representation of a system of linear equations?

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) to the system.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method 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

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

Front

What does it mean for two lines to be coincident?

Back

Two lines are coincident if they lie on top of each other, meaning they have infinitely many solutions.

Front

How do you find the intersection point of two lines given by equations?

Back

To find the intersection point, solve the equations simultaneously using substitution or elimination to find the values of x and y.

Front

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

Back

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