Solving Linear Equations and Systems - basics

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable that makes the equation true.

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.

Front

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

Back

You can find the solution by graphing the equations and identifying the point of intersection, or by using substitution or elimination methods.

Front

What is the substitution method in 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 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 if two lines are parallel in a system of equations?

Back

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

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

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If two lines are coincident, it means they lie on top of each other, indicating that there are infinitely many solutions to the system.

Front

Solve for x: 7x - 3x - 8 = 24

Back

x = 8

Front

Solve for x: 3(5x + 1) = 48

Back

x = 3