Find x and y using the equations 3x + y= 10, x + y = 4
First of all there are 3 different methods of working out simultaneous equations: Elimination, Substitution and Graphical. Today I will show the substitution method.
If x + y = 4 then rearranging the equation y = 4 - x Now that I have found an equation for y I can SUBSTITUTE it into the other equation 3x + y = 10Therefore 3x + 4 - x = 10 I did this so that I could have an equation where the is only one unknown variable. This makes it easy to work out So by collecting like terms 2x + 4 = 10 Rearranging this equation gives us 2x = 6 Therefore x = 3
Now that I have found x it is easy to find y since I can substitute x into any of the original equations I had to find a value of y.
x + y = 4x = 3 therefore 3 + y = 4Rearrange the equation and y = 1
To check that you are right input the values into the second equation and make sure the values on both sides are equal
3x + y = 103 x 3 + 1 = 10 9 + 1 = 1010= 10Therefore my values for x and y are correct!
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