SOLUTION: x+y=12 x-7=4 how do u go about solving a question like this??

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Question 173215This question is from textbook Amsco's integrated algerbra 1
: x+y=12
x-7=4

how do u go about solving a question like this?? This question is from textbook Amsco's integrated algerbra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm assuming that you left out the variable "y" in the second equation and it should look like x-7y=4






Start with the given system of equations:

system%28x%2By=12%2Cx-7y=4%29


Let's solve this system by use of substitution



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

x%2By=12 Start with the first equation


y=12-x Subtract x from both sides


y=-x%2B12 Rearrange the equation


---------------------

Since y=-x%2B12, we can now replace each y in the second equation with -x%2B12 to solve for x



x-7highlight%28%28-x%2B12%29%29=4 Plug in y=-x%2B12 into the second equation. In other words, replace each y with -x%2B12. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2B%28-7%29%28-1%29x%2B%28-7%29%2812%29=4 Distribute -7 to -x%2B12


x%2B7x-84=4 Multiply


8x-84=4 Combine like terms on the left side


8x=4%2B84Add 84 to both sides


8x=88 Combine like terms on the right side


x=%2888%29%2F%288%29 Divide both sides by 8 to isolate x



x=11 Divide





-----------------First Answer------------------------------


So the first part of our answer is: x=11









Since we know that x=11 we can plug it into the equation y=-x%2B12 (remember we previously solved for y in the first equation).



y=-x%2B12 Start with the equation where y was previously isolated.


y=-%2811%29%2B12 Plug in x=11


y=-11%2B12 Multiply


y=1 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=1









-----------------Summary------------------------------


So the solutions are:


x=11 and y=1


which form the ordered pair