Solve 2x + 3y = 11 and x - y = -7 using any method. Explain your choice.
2007-11-26 03:38:48 · 6 answers · asked by Lilsleepy59 3 in Science & Mathematics ➔ Mathematics
2x + 3y = 11
x -y = -7
OK let's use substitution :
x= -7+y
2(-7+y) + 3y = 11
-14 +2y + 3y = 11
5y = 25
y = 5
Now substitute in equations
x - 5 = -7
x = -2
Do check in first equation
2(-2) + 3(5) = 11 ??
-4 + 15 = 11??
11=11 YES!!
I chose the substitution method because we had one of the equations with a simple x and y so it was easy to put the x in terms of y.
Hope that helps.
2007-11-26 03:44:32 · answer #1 · answered by pyz01 7 · 0⤊ 1⤋
Substitution:
Take x - y =-7 and solve for x (add y to both sides)
x= y-7. (Now substitute this equation in for x in the other equation)
2(y-7) + 3y = 11 ( distribute the 2)
2y - 14 + 3y = 11 (add the y's)
5y - 14 =11 (add 14 to each side)
5y = 25 (divide each side by 5)
y = 5
Now that you have y substitute it into the equation of your choice to get x
x-5 =-7 ( add 5 to both sides)
x= -2
(-2,5)
I chose substitution because the second equation's x and y had no coefficents making it easy to use substitution.
2007-11-26 03:59:38 · answer #2 · answered by Laynett 2 · 0⤊ 1⤋
2x + 3y=11 -----------Equation 1
x - y=-7 -----------Equation 2
multiply eq 1 with 1 and eq 2 with 2 so that the at least one of the variables of the degrees are equal...
you would get...
2x + 3y=11 eq 3
2x - 2y=-14 eq 4
now subtract eq 4 from eq 3
2x + 3y = 11
- (-)2x - (+)2y = -(+)14
5y = 25
y = 25/5
y=5
now substituting the value of y in eq 2
x - 5 = -7
x = -7 + 5
x = -2
hence your answer
x = -2 and y=5
2007-11-26 04:09:00 · answer #3 · answered by killer 1 · 0⤊ 1⤋
2X + 3Y = 11---------(i)
X - Y = -7----------(ii)
multiply thru (ii) by 3 and add (i)
(2X + 3Y = 11)
+
(3X - 3Y = -21)
5X = -10,THUS X = -2
Therefore Y = 5
X= -2,y = 5
Reason,its the 1st and simplest rule for linear equation solving.And its advantage is that u get to cancel out one unknown value making the whole thing a smooth operation.
2007-11-26 03:48:12 · answer #4 · answered by Duse 3 · 0⤊ 1⤋
2x+3y = 11
x-y=-7
-y = -7 -x
y = x+7
substitute
2x + 3(x+7 ) =11
2x + 3x + 21 = 11
5x = 11-21 = -10
x = -2
y=x+7 = -2 + 7
y= 5
2007-11-26 03:43:37 · answer #5 · answered by Grant d 4 · 1⤊ 0⤋
2x + 3y = 11
- 2x + 2y = 14-----ADD
5y = 25
y = 5
x - 5 = - 7
x = - 2
x = - 2 , y = 5
2007-11-26 04:00:14 · answer #6 · answered by Como 7 · 1⤊ 1⤋