Find value of x and y in :
1/7x + 1/6y =3
1/2x - 1/3y =5
BY SUBSITUTING METHOD.
1/6 y = 3 - 1/7 x
so,
1/3 y = 6 - 2/7 x
Now use that in the other equation:
1/2 x - (6 - 2/7 x) = 5
11/14 x = 11
x = 14
or, you can use elimination.
since 1/3 = 2/6,
2/7 x + 1/3 y = 6
1/2 x - 1/3 y = 5
Now add the two equations to get rid of the y:
11/14 x = 11
so, x = 14
Now use that to find y.
qwerty
To solve the given system of equations using the substitution method, we need to express one variable in terms of the other in one of the equations and substitute that expression into the other equation.
Let's solve the first equation for x:
1/7x + 1/6y = 3
Multiply both sides of the equation by 7 to eliminate the fraction:
7 * (1/7x + 1/6y) = 7 * 3
1x + 7/6y = 21
x + (7/6)y = 21
Next, solve the second equation for x:
1/2x - 1/3y = 5
Multiply both sides of the equation by 2 to eliminate the fraction:
2 * (1/2x - 1/3y) = 2 * 5
1x - 2/3y = 10
x - (2/3)y = 10
Now, we have the expressions for x in both equations:
x + (7/6)y = 21 (Equation 1)
x - (2/3)y = 10 (Equation 2)
Since we want to solve by the substitution method, we can rearrange Equation 1 to get x in terms of y:
x = 21 - (7/6)y
Now, substitute this expression for x in Equation 2:
x - (2/3)y = 10
(21 - (7/6)y) - (2/3)y = 10
Simplify the equation:
21 - (7/6)y - (2/3)y = 10
21 - (21/6)y - (4/6)y = 10
21 - (25/6)y = 10
- (25/6)y = 10 - 21
- (25/6)y = -11
Now, to solve for y, multiply both sides of the equation by -6/25 to isolate y:
y = (-11) * (-6/25)
y = 264/25
Now that we have the value of y, substitute it back into Equation 1 to solve for x:
x = 21 - (7/6)y
x = 21 - (7/6) * (264/25)
x = 21 - (7 * 264)/(6 * 25)
x = 21 - 1848/150
x = 21 - 92/75
x = (75 * 21 - 92)/75
x = (1575 - 92)/75
x = 1483/75
Therefore, the solution to the system of equations is x = 1483/75 and y = 264/25.