How do you solve linear equations ?

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tjbrewer's profile pic

tjbrewer | Elementary School Teacher | (Level 2) Associate Educator

Posted on

It is unclear what you mean by solving linear equations, but I will endeavour to help. 

Linear equations are algebraic expressions that form a straight line when plotted on a graph, hence the term 'linear.' 

The most common "solves" associated with such equations:

  • You are given two points as ordered pairs, and asked to find the line that goes through them.  You use the slope formula `(y_2-y_1)/(x_2-x_1) ` to find the slope of the line, then solve for one of the points to find the x-intercept.  You now have the equation in slope intercept form, and now you just transpose the variables into the form the question specifies
  • You are given a linear equation, and a value for one of the variables, and asked to find the value of the other variable.  You simply insert the value you are given for the appropriate variable, isolate the other variable and solve to find that variable's value
  • You are given two equations and asked to find where they intersect.  You should isolate the same variable (usually y) in each equation, set them equal to each other, and find the other variable (usually x).  Then solve each equation for that variable to verify that they both yield the same value for y.  If they don't, or if no value for x exists that will make the equation true, then the lines do not intersect. 

Repost with a more specific problem in order to receive a more relevant answer. 

mchandrea's profile pic

mchandrea | Student, College Junior | (Level 1) Salutatorian

Posted on

Linear equations, as the name denotes are equations for straight lines. There are numerous types of linear equations which means there are also different methods of solving them. Linear equations often have constants and variables. And these variables do not  have exponents or square roots or cubed roots, etc.

The general equation is `Ax + By + C = 0` 

Some other types of equation are:

a. Slope Intercept Form ---> y = mx + b where m is the slope and b is the y-intercept

b. Point Slope Form ---> y - y1 = m (x-x1)

There are still different forms of equation and each one will have a different way in solving. But what is common to all would be, you have to have the value for  x and y intercept and the slope. 

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zumba96's profile pic

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

Posted on

By linear equations I'm assuming you mean ones like x+3=5 and so on? You always want to get x by itself, you'll probably hear this phrase dozens of times but its very important. Try to isolate the variable and then afterward solve

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