find the solution of this system of equation
find the solution of this system of equation
Skyrie did an excellent job of creating a step by step solution, and she has my vote. Having said that, there is a shortcut.
-5x + y = -7
6x - y = 7
Just add the two equations. The y's cancel out. -7 and 7 also cancel out.
-5x + y + 6x - y = x
x = -7 + 7 = 0
-5(0) + y = 0 + y = y = -7
Check: 6x - y = 6(0) - (-7) = 0 + 7 = 7
This is a system of equation. I will go over it step by step so that you will understand what is going on.
{-5x+y=-7}
{-6x-y=7}
I would first give (y) a meaning, so then I can use it for substitution later. I will use the equation (-5x+y=-7).
-5x+y=-7
+5x +5x <==== I added 5x on both sides so that I can have y alone
y= -7+5x <===== The y is now equal to -7+5x, I will use this for my other equation (-6x-y=7).
I will substitute y from -6x-y=7 and replace it with my new equation -7+5x.
-6x-(-7+5x)=7 <=== remember to make the equation nice and neat for you to understand, fix your negative and positive signs.
-6x+7-5x=7 <==== when you multiply two negatives it makes a positive, however, multiplying a negative and a positive makes a negative.
(-6x-5x)+7=7 <=== combine like terms
-11x+7=7 <=== remember (keep switch change) you keep -6x switch the negative to a positive and change the positive 5 to a negative 5. ( This only applies when you are subtracting or adding number)
-11x+7=7
-7=-7 <=== I subtracted 7 on both sides so that I can have x alone
-11x=0
-11 -11 <==== I divided -11 on both sides ( 0 divided by any number equals to 0, but it is impossible to divide a number by 0 it would be undefined check on you calculator)
x=0
Now we will solve for y...
I will use what I know and plug it in.
-6x-y=7
-6(0)-y=7 <=== x=0 remember
-y=7 <=== 0 times any number equal 0
-1 -1 <=== when a variable exist but it has no number in front of it there is an imaginary 1 in front of the variable.
y= -7
x=0
Now let's check our answer
-5x+y=-7
-5(0)+(-7)=-7
-7=-7 yes it worked
-6x-y=7
-6(0)-(-7)=7
7=7 yes it worked
X=0
Y=-7
Comments
I love the technique you used I never thought of it that way. I would love to use that technique if you do not mind.