2x + 3y = 2 x - 3y = 7 find x and y
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2x + 3y = 2 ........(1)
x - 3y = 7 ..........(2)
Using the elimination method, add both (1) and (2):
==> 3x = 9
==> divide by 3:
==> x = 3
Now to find y value using the substitution method, we will substitute with either (1) or (2)
x - 3y = 7
==> 3y = x-7
==> y = (x-7)/3 = (3-7)/3 = -4/3
==> y = -4/3
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2x + 3y = 2
x - 3y = 7
3x=9
x=3
x-3y=7
3-3y=7
-3y=4
y=-4/3
2x + 3y = 2
x - 3y = 7
First multiply everything in the bottom equation by 2
By multiplying, you should get
2x + 3y = 2
2x - 6y = 14 now subtract 2x with 2x ( which means subtract 3y with -6y and 2 with 14 )
By subtracting, you should get
9y = -12 divide both sides by 9
By dividing, you should get
Y = -12/9 simplify
Y = -4/3 which is your answer for " y "
Now plug -4/3 into one of the equation
X - 3 ( -4/3 ) = 7 multiply -3 with -4/3
By multiplying, you should get
X + 12/3 = 7 subtract 12/3 on both sides
By subtracting, you should get
X = 4 which is your answer for " x "
So x = 4 and y = -4/3
Elimination process:
2x + 3y = 2
+ x - 3y = 7 Eliminate 3y since 3y + -3y = 0
3x = 9
3x/3 = 9/3 divide 3x and 9 by 3 to eliminate 3
x= 3
then, substitute the value of the x to any of the given equations.
2(3) + 3y = 2
6 + 3y = 2 multiply 2 and 3
3y = 2 - 6 move 6 to the other side
3y/3 = -4/3 divide 3y and -4 by 3
y= -4/3
Because the equations of the system are linear, we'll use the matrix formed by the coefficients of the variables to calculate the determinant of the system:
2 3
det A =
1 -3
det A = 2*(-3) - 3
det A = -6 - 3
det A = -9 different from zero.
Now, we'll calculate x:
x = det x/ det A
2 3
det x =
7 -3
det x = -6 - 21 = -27
x = -27/-9
x = 3
Now, we'll calculate y:
2 2
det y =
1 7
det y = 14 - 2
det y = 12
y = det y/ det A
y = 12/-9
y = -4/3
The solution of the system is: {(3 , -4/3)}
2x+3y = 2
x-3y =7.
Tofind x and y.
Solution:
We use substitution method.
From the 2nd equation, we get x = 7+3y. Substuting this in the first, we get 2(7+3y) + 3y = 2.
14+6y +3y =2
14+ 9y = 2
9y = 2-14 = -12.
y = -12/9 = -4/3
Substituting y =-4/9 in 2nd equation, x-3(-4/3) = 7, x = 7+3*(-4/3) = 3
x = 3 and y = -4/3
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