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How to Solve A System of Equations

When you have two equations with two variables you need a system of equations.

For example:


Equation 1: X - Y = 8


Equation 2: X - 2Y= - 20


From equation 1 solve for one variable,


(choose the easiest one to solve, in this case "X")


X - Y = 8

X= Y + 8


Now substitute it into equation 2


X - 2Y = 20


(Y + 8 ) - 2Y= -20


-Y + 8= -20


-Y= -20 - 8


-Y= -28


Y= 28


Find the value of "X" by substituting Y=28 into the first equation


X= 28 + 8 = 36
X= 36


You can verify your answer by substituting your values into the original equation


36 - 28 = 8
36- 2(28) = - 20


Practice Problems: