Linear Equations

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Cramer’s Rule for Linear Algebra

Named for Gabriel Cramer, Cramer’s Rule provides a solution for a system of two linear algebraic equations in terms of determinants — the numbers associated with a specific, square matrix. [more…]

Solving Absolute-Value Equations

A linear absolute value equation is an equation that takes the form |ax + b| = c. Taking the equation at face value, you don’t know if you should change what’s in between the absolute value bars to its [more…]

How to Solve Linear Equations with Division

A basic method for solving linear equations is to divide each side of the equation by the same number. Many formulas and equations include a coefficient, or multiplier, with the variable. To get rid of [more…]

How to Solve Linear Equations with Multiplication

To solve linear equations with multiplication, you first determine that division is being used in the linear equation. Multiplication is the inverse (opposite) operation of division, so you can use multiplication [more…]

How to Solve Linear Equations with Both Multiplication and Division

Often, you need to use both multiplication and division to solve a linear equation. When a linear equation uses both multiplication and division, you solve by using the inverse operation of each. So, if [more…]

How to Solve Linear Equations with Reciprocals

You can use the reciprocal of the number that you’re trying to “get rid of” if a fraction is multiplying the variable. You solve linear equations with reciprocals when you see a fraction — it's easier [more…]

Calculator Commands for Linear Algebra

Graphing calculators are wonderful tools for helping you solve linear algebra processes; they allow you to drain battery power rather than brain power. Since there is a wide variety of graphing calculators [more…]

How to Meet Vector Space Requirements

In linear algebra, a set of elements is termed a vector space when particular requirements are met. For example, let a set consist of vectors u, v, and [more…]

Algebraic Properties You Should Know

You can use a number of properties when working with linear algebraic expressions, including the commutative, associative, and distributive properties of addition and multiplication, as well as identities [more…]

Systems of Linear Equations in Algebra II

In Algebra II, a linear equation consists of variable terms whose exponents are always the number 1. When you have two variables, the equation can be represented by a line. With three terms, you can draw [more…]

Linear Equations: How to Find Slope, y-Intercept, Distance, Midpoint

In algebra, linear equations means you're dealing with straight lines. When you're working with the xy-coordinate system, you can use the following formulas to find the slope, [more…]

Rewrite Absolute Value Equations as Linear Equations

To work with an absolute value equation in algebra, you first need to rewrite it as a linear equation. The same goes for an absolute value inequality, which you rewrite as a linear inequality. [more…]

Systems with Three Linear Equations

When working with systems of equations, you can solve for one variable at a time. So, if a third linear equation comes along (bringing, of course, its variable [more…]

Finding the Intersections of Lines and Parabolas

A line can cut through a parabola in two points, or it may just be tangent to the parabola and touch it at one point. And then, sadly, a line and a parabola may never meet. When solving systems of equations [more…]

Crossing Curves: Finding the Intersections of Parabolas and Circles

When a parabola and circle intersect, the possibilities for their meeting are many and varied. The two curves can intersect in as many as four different points, or maybe three, or just two or even just [more…]

Solving Two Linear Equations Algebraically

A solution of a system of two linear equations consists of the values of x and y that make both of the equations true — at the same time. Graphically, the solution is the point where the two lines intersect [more…]

How to Solve Simple Linear Equations in Algebra

Solving linear equations in algebra is done with multiplication, division, or reciprocals. Using reciprocals, or multiplicative inverse, as well as multiplying and dividing with certain formulas, you can [more…]
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