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- Start by looking just at the first equation. Rearrange it by subtracting 2y from each side, to get: 4x = 8 - 2y. This method often uses fractions later on. You can try the elimination method below instead if you don't like fractions. Divide both sides of the equation to "solve for x."
www.wikihow.com/Solve-Systems-of-Algebraic-Equations-Containing-Two-Variables4 Ways to Solve Systems of Algebraic Equations Containing Two ...
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Move the variables to different sides of the equation. This "substitution" method starts out by "solving for x" (or any other variable) in one of the equations.[2] X Research source For example, let's say your equations are 4x + 2y = 8 and 5x + 3y = 9. Start by looking just at the first equation. Rearrange it by subtracting 2y from each side, to get: 4x = 8 - 2y. This method often uses ...Divide both sides of the equation to "solve for x. " Once you have the x term (or whichever variable you are using) on one side of the equation, divide both sides of the equation to get the variable alone.[3] X Research source For example: 4x = 8 - 2y (4x)/4 = (8/4) - (2y/4) x = 2 - ½yPlug this back into the other equation. Make sure you go back to the other equation, not the one you've already used.[4] X Research source In that equation, replace the variable you solved for so only one variable is left. For example: You know that x = 2 - ½y. Your second equation, that you haven't yet altered, is 5x + 3y = 9. In the second equation, replace x with "2 - ½y": 5(2 - ½y ...Solve for the remaining variable. You now have an equation with only one variable. Use ordinary algebra techniques to solve for that variable.[5] X Research source If your variables cancel out, skip ahead to the last step. Otherwise, you'll end up with an answer for one of your variables: 5(2 - ½y) + 3y = 9 10 – (5/2)y + 3y = 9 10 – (5/2)y + (6/2)y = 9 (If you don't understand this step ...Use the answer to solve for the other variable. Don't make the mistake of leaving the problem half-finished. You'll need to plug the answer you got back into one of the original equations, so you can solve for the other variable:[6] X Research source You know that y = -2 One of the original equations is 4x + 2y = 8. (You can use either equation for this step.) Plug in -2 instead of y: 4x + 2 ...You can check your work by plugging the answers back into the original equations. If the equations end up true (for instance, 3 = 3), your answer is correct. Thanks Helpful 4 Not Helpful 1In the elimination method, you will sometimes have to multiply one equation by a negative number in order to get a variable to cancel out. Thanks Helpful 1 Not Helpful 1These methods cannot be used if there is a variable raised to an exponent, such as x2. For more information on equations of this type, look up a guide to factoring quadratics with two variables.[11] X Research source Thanks Helpful 1 Not Helpful 0- 1.1M
Jan 27, 2023 · To solve a simple linear equation, start by moving the numbers with a variable attached to one side of the equation and the numbers without a variable attached to the other side. To move a number to a different side, you need to subtract it from both sides.
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