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The linear equations in two variables are the equations in which each of the two variables is of the highest order (exponent) of 1 and may have one, none, or infinitely many solutions. The standard form of a two-variable linear equation is ax + by + c = 0 where x and y are the two variables.
In Solving Linear Equations, we learned how to solve linear equations with one variable. Now we will work with two or more linear equations grouped together, which is known as a system of linear equations.
Two-variable linear equations intro. Solutions to 2-variable equations. Worked example: solutions to 2-variable equations. Solutions to 2-variable equations. Completing solutions to 2-variable equations. Complete solutions to 2-variable equations.
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There are three types of systems of linear equations in two variables, and three types of solutions. An independent system has exactly one solution pair \ ( (x,y)\). The point where the two lines intersect is the only solution. An inconsistent system has no solution.
To solve a system of two linear equations, we want to find the values of the variables that are solutions to both equations. In other words, we are looking for the ordered pairs \((x,y)\) that make both equations true.
Learn how to solve linear equations in two variables using graphs, substitution method, and word problems. Find out the conditions for unique, no, or infinite solutions and the system of linear equations.
