Answer:
(x,y) = (-2,3)
Explanation:
First lets match up the variables and cancel one out in order to solve for x or y. By cancelling either an x or y we can get an equation just in terms of either variable and solve for either one from there.
First, lets multiply the first equation -2x+3y =13 by 3 and the second equation 3x+4y = 6 by 2.
This will give us:
-6x+9y = 39
6x+8y = 12
we can now see that the x terms are the same but since the first equation is negative when we add the x terms together we get -6x + 6 = 0
when we add the y terms we get 17y
finally when we add 39 + 12 we get 51.
From there we are left with 17y on the left hand side and 51 on the right hand side
17y = 51
in order to solve for y we divide both sides of the equation by 17 giving us : (y = 51/17) 51/17 = 3 so,
- y=3
now that we have found y we can plug this in either one of the two original equations.
In this case I will plug in y = 3 into the second equation,
doing this will give the result: 3x+4(3) = 6
Simplifying : 3x+12 = 6
in order to solve for x we have to isolate it by itself on the left hand side.
we can move the 12 from the left side by subtracting it from the left hand side and subtracting it from the right hand side also.
giving us 3x = -6
from here we can divide by 3 giving us the result x = -2.
Thus the order pair that satisfies the system of equations is:
(-2,3)
I hope this helps!