Question 650978: hi,im a student 15 years old, having trouble with finding the solution to this question.
6x + 5y = 7 & x - y = 3
i have to find the coordinates (x,y) i found that the answer is x= 2 and y = -1
but i dont know how to find the soulution. Please help thanks.
Found 2 solutions by nerdybill, DrBeeee:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 6x + 5y = 7 & x - y = 3
.
apply the "substitution method", solve the right equation for x:
x - y = 3
x = y+3
substitute above into the left equation to find y:
6x + 5y = 7
6(y+3) + 5y = 7
6y+18 + 5y = 7
11y+18 = 7
11y = -11
y = -1
.
substitute above into the right equation to find x:
x - y = 3
x - (-1) = 3
x + 1 = 3
x = 2
.
solution: (x,y) = (2, -1)
Answer by DrBeeee(684)  (Show Source):
You can put this solution on YOUR website! Good point," I have the answer but not the solution." I wish all my students would realize the difference. By the way, the point (2,-1) is correct. There are a at least two ways to solve the problem, I'll show you the one called,"solve by substitution." You are given two equations in two variables, x and y,
(1) 6x + 5y = 7 and
(2) x - y = 3
Your first step is to solve one of the equations for one of the variable in terms of the other variable. Since (2) is simpler than (1), let's solve (2) for x, yielding
(3) x = 3 + y, OK?
Now we substitute (3) into (1), ergo the substitution method, and get
(4) 6*(3 + y) + 5y = 7; note that you now have only one equation in a single variable.
Simplify (4) to get
(5) 18 + 6y + 5y = 7 or
(6) 11y = -11, OK? Then
(7) y = -1
Now put y = -1 into (2) and get
(8) x - (-1) = 3 or
(9) x = 2
Our point is (2,-1), but is it correct?
Now always check your answer! Since we used (2) to derive the value of x, check the solution with (1).
Is (6*(2) + 5*(-1) = 7)?
Is (12 - 5 = 7)?
Is (7 = 7)? Yes
Answer: The solution pair is (2,-1)
Make sense? To apply the substitution method you must be adept at simplifying algebraic equations. Otherwise it's straight forward.
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