2x-3y = 8 x+2y=3 solve x and y
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2x-3y =8......(1)
x+2y =3.......(2)
We will use the elimination method to solve:
First, multiply (2) by -2 and add to (1):
-7y = 2
==> y= -2/7
Now substitute y= -2/7 in (2):
x+ 2y= 3
x+ 2(-2/7) = 3
x -4/7= 3
Move -4/7 to the right side:
x= 3+ 4/7
x= 21/7 + 4/7 = 25/7
x= 25/7
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2x - 3y = 8
x + 2y = 3
multiply the digits on the second equation by 2
By multiplying, your equation should look like
2x - 3y = 8
2x + 4y = 6
Now, subtract the 2x with 2x ( so subtract -3y with 2y and 8 with 6 )
By doing that your equation should look like
-7y = 2 now divide both sides by -7
By dividing, your equation should look like
y = -2/7 which is your answer for " y "
Now, plug - 2/7 into one of the equation
2x + 4 ( -2/7 ) = 6 multiply 4 with -2/7
By multiplying, your equation should look like
2x - 8/7 = 6 add 8/7 on both sides
By adding, your equation should be
2x = 50/7 divide both sides by 2
By dividing, your equation should look like
x = 50/14 simplify
x = 25/7 which is your answer for " x "
So, your answer is x = 25/7 ; y = -2/7
We'll eliminate the unknown y, by multiplying the first equation by 2 and the second equation, by 3.
The system of equations will become:
2(2x-3y) = 16
3(x+2y) = 9
Now, we'll open the brackets and we'll add the equations from the system:
4x - 6y + 3x + 6y = 16+9
7x = 25
We'll divide by 7:
x = 25/7
We'll find y, substituting x by it's value, in any of 2 equations.
We'll substitute x in the first equation:
2x-3y = 8
50/7 - 3y = 8
-3y = 8 - 50/7
-3y = (56-50)/7
-3y = 6/7
We'll divide by -3:
y = 6/-3*7
y = -2/7
The solution of the system is: (-2/7 , 25/7).
2x - 3y = 8 ... (1)
x + 2y = 3 ... (2)
Multiplying equation (2) by 2 :
2x + 4y = 6 ... (3)
Subtracting equation (1) from (3):
2x - 2x + 4y + 3y = 6 - 8
7y = -2
y = -2/7
Substituting value of y in equation (2):
x + 2(-2/7) = 3
x - 4/7 = 3
x = 3 + 4/7 = 25/7
Answer:
x = -2/7, y = 25/7
To solve
2x-3y = 8......(1)
x+2y=3 ........(2)
Solution:
We solve by substitution method using y value from eq(2) and put it in (1).
From (2) we get: y =(3-x)/2. Put this value of y in (1) and get:
2x - 3(3-x)/2 = 8. Multiply by 2.
4x-3(3-x) = 6.
4x-9+3x = 16
7x = 16+9 = 25
7x+7 =25/7
x=25/1 = 3 and 4/7.
Substituting this in (1), 2x-3y = 8, 2(25/7)-3y = 8, -3y = 8-50/7 = 6/7, y = (6/7)/(-3) = -2/7.
So (x,y) = (25/7,-2/7)
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