SOLUTION: 1.solve the system by addition. -2x+3y=-15 x-2y=11 I got -x+y=-4 that doesn't seem right. 2.The difference of two numbers is 27. The second is 1 less than 3 times the f

Algebra ->  Linear-equations -> SOLUTION: 1.solve the system by addition. -2x+3y=-15 x-2y=11 I got -x+y=-4 that doesn't seem right. 2.The difference of two numbers is 27. The second is 1 less than 3 times the f      Log On


   

Question 74108: 1.solve the system by addition.
-2x+3y=-15
x-2y=11
I got -x+y=-4 that doesn't seem right.


2.The difference of two numbers is 27. The second is 1 less than 3 times the first. What are the two numbers?


3.solve the following system of linear inequalities by graphing.
3x+4y is less than or equal to 12
x+3y is less than or equal to 6
x is greater than or equal to 0
y is greater than or equal to 0
Sorry, i'm not sure how to show the lees than and greater than symbols.
I'd appreciate any help you could give me

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1.
You need to have either x or y have the same but opposite coefficients in order to eliminate them. 

             -2x+3y=-15
              2(x-2y)=2(11)     <--------Multiply both sides by 2
                                    


             -2x+3y=-15
              2x-4y= 22     <--------Add the 2 equations
         -----------------
              0x -y=7

So y=-7 and x equals
x-2%28-7%29=11
x=11-14
x=-3


Check:


             -2(-3)+3(-7)=-15
               (-3)-2(-7)=11     Plug in (-3,-7)
                                    


                   6+-21=-15
               (-3)+14=11     Plug in (-3,-7)
                                    


                   -15=-15            Works
                    11=11             Works

So (-3,-7) is the solution.


2.
Let f=1st # and s=2nd #
Here's the translated word problem
s-f=27"difference of two numbers is (=) 27"
s=3f-1"second (s) is (=) 1 less (-) than 3 times the first (3f)
s=27%2BfSolve for s, plug this into s=3f-1
27%2Bf=3f-1
28=2f
f=14
So the 1st number is 7 the 2nd number is:
s=27%2B14
s=41


Check:
41-14=27
27=27works
41=3%2814%29-1
41=41works


3.
To solve the system graphically, we need to graph the inequalities. To do this we must make them an equation and solve for y
3x%2B4y%3C=12Solve for y
3x%2B4y=12Make an equation
4y=12-3xSubtract 3x from both sides
y=3-%283%2F4%29xDivide both sides by 4. Now we can graph this equation
x%2B3y%3C=6Solve for y
x%2B3y=6Make an equation
3y=6-xSubtract x from both sides
y=2-%281%2F3%29xDivide both sides by 3. Now we can graph this equation
Since x and y is greater than x, we only need to graph these equations in the 1st quadrant (the upper left portion of the graph). So the graphs look like
graph%28+300%2C+200%2C+0%2C+7%2C+0%2C+10%2C+2-%281%2F3%29x%2C+3-%283%2F4%29x%29+
To complete this we need to test which points will satisfy this set of inequalities. Let's try (0,0) plug this into 3x%2B4y%3C=12
3%280%29%2B4%280%29%3C=12
0%3C=12Which is true
Now try (0,0), plug this into x%2B3y%3C=6
0%2B3%280%29%3C=6
0%3C=6Which is true. This means you shade the region that contains (0,0) for both inequalities, which is below the graph for both. Since these regions overlap, you would ultimately shade their overlapping region, which is bounded by the x and y axises and the lines. If you want a picture email me and I'll send you one to give you an idea of what it looks like. Hope this helps.