SOLUTION: y = 3x + 7 y = -4x + 21

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Question 1173247: y = 3x + 7
y = -4x + 21

Found 3 solutions by ewatrrr, ikleyn, MathTherapy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi  

y = 3x + 7

y = -4x + 21

solving this System of Equations:

y  -3x = 7

y + 4x = 21     |Multiplying the 1st EQ by -1 to eliminate y



-y + 3x = -7

y + 4x = 21

   7x = 14

x = 2   and we know y = 3x + 7  y+=3%2A2%2B7 y = 13

Ordered Pair P(2,13) is the solution for this system of Equations

Wish You the Best in your Studies.

Sketching the two Lines and showing their Intersection

y = 3x + 7 (Green)      y = -4x + 21 (Blue)  Note it slants to the left(negative slope)

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

            When I see a system of equations like this one,  I have ready and I use my standard mantra.  It says: 


The two given equations have identical left sides - - - hence, their right sides are equal

    3x + 7 = -4x + 21.


From this equation

    3x + 4x = 21 - 7

      7x    =    14

       x    =    14/7 = 2.


Then y = 3x + 7 = 3*2 + 7 = 6 + 7 = 13.


ANSWER.  x= 2,  y= 13.

Solved.

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

My mantra is short and makes the solution short - - - THEREFORE,  I like it  (!)

You may use it,  too  (!)



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

y = 3x + 7
y = -4x + 21
y =   3x + 7 ----- eq (i)

y = - 4x + 21 ---- eq (ii)

0 = 7x - 14 ------ Subtracting eq (ii) from eq (i)

14 = 7x

highlight_green%28matrix%281%2C5%2C+14%2F7%2C+%22=%22%2C+x%2C+%22=%22%2C+2%29%29

Now you can find y.