Systems of Linear Equations

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 two lines to intersect in a graph of linear equations?

Back

When two lines intersect, it means that there is a common solution to the system of equations represented by those lines. The coordinates of the intersection point are the values of the variables that satisfy both equations.

Front

How can you estimate the solution of a system of linear equations from a graph?

Back

You can estimate the solution by identifying the point where the two lines intersect on the graph. This point gives the values of the variables that solve both equations.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 4?

Back

The solution is (1, 3), where the two lines intersect.

Front

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

Back

If two lines are parallel, it means they have the same slope but different y-intercepts, indicating that there is no solution to the system of equations.

Front

What is the graphical representation of a linear equation?

Back

A linear equation can be represented graphically as a straight line on a coordinate plane, where the x-axis represents the independent variable and the y-axis represents the dependent variable.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run). It indicates how much y changes for a unit change in x.

Front

What is the y-intercept of 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 zero.

Front

How do you solve a system of linear equations using substitution?

Back

To solve by substitution, solve one equation for one variable and then substitute that expression into the other equation to find the value of the second variable.

Front

How do you solve a system of linear equations using elimination?

Back

To solve by elimination, add or subtract the equations to eliminate one variable, making it easier to solve for the remaining variable.