1/2x+1/3y=5 sub 1/4x+y=0
If you mean you want to solve the system of equations
1/2x+1/3y = 5
1/4x+y = 0
by substitution, then substitute y = -1/4 x into the 1st equation and you have
1/2 x + 1/3 (-1/4 x) = 5
1/2 x - 1/12 x = 5
5/12 x = 5
x = 12
and y = -1/4 x = -3
1/2x + 1/3y = 5, and 1/4x + y = 0.
Multiply the 1st Eq. by 6 and the 2nd Eq. by 12 and subtract:
Eq1: 3x + 2y = 30.
Eq2: 3x + 12y = 0.
Diff,: -10y = 30,
Y = -3.
In Eq1, replace Y with --3 and solve for X:
3x + 2(-3) = 30.
X = 12.
To solve the system of equations:
1/2x + 1/3y = 5 ............(Equation 1)
1/4x + y = 0 ............(Equation 2)
There are several methods to solve this system of equations, such as substitution, elimination, or by using matrices. Let's solve it by the method of substitution.
Step 1: Solve Equation 2 for x:
1/4x + y = 0
Subtract y from both sides:
1/4x = -y
Multiply both sides by 4 to get rid of the fraction:
x = -4y
Step 2: Substitute the value of x into Equation 1:
1/2x + 1/3y = 5
Replace x with -4y:
1/2(-4y) + 1/3y = 5
Simplify:
-2y + 1/3y = 5
Combine like terms:
(-2y + 1/3y) = 5
(-6y + y) / 3 = 5
-5y / 3 = 5
Multiply both sides by 3 to eliminate the fraction:
-5y = 3 * 5
-5y = 15
Step 3: Solve for y:
Divide both sides by -5:
y = 15 / -5
y = -3
Step 4: Substitute the value of y back into Equation 2 to solve for x:
1/4x + y = 0
Substitute y with -3:
1/4x + (-3) = 0
1/4x - 3 = 0
Add 3 to both sides:
1/4x = 3
Multiply both sides by 4:
x = 3 * 4
x = 12
Step 5: Check the solution by substituting the values of x and y into Equation 1:
1/2x + 1/3y = 5
Substitute x with 12 and y with -3:
1/2(12) + 1/3(-3) = 5
6 + (-1) = 5
5 = 5
The values x = 12 and y = -3 satisfy both equations, so the solution to the system of equations is x = 12 and y = -3.
If your question mean:
1 / 2 x +1 / 3 y = 5 , 1 / 4 x + y = 0
then
1 / 2 x +1 / 3 y = 5
Multiply both sides by 1 / 2
1 / 4 x +1 / 6 y = 5 / 2
1 / 4 x + 1 / 6 y = 5 / 2
-
1 / 4 x + y = 0
________________
0 + 1 / 6 y - y = 5 / 2 - 0
1 / 6 y - 6 / 6 y = 5 / 2
- 5 / 6 y = 5 / 2
Divide both sides by 5
- 1 / 6 y = 1 / 2
- y / 6 = 1 / 2
Cros multiply
- y ∙ 2 = 6 ∙ 1
- 2 y = 6
Divide both sides by - 2
y = 6 / - 2
y = - 3
Replace this value in equation 1 / 4 x + y = 0
1 / 4 x + ( - 3 ) = 0
x / 4 - 3 = 0
Add 3 to both sides
x / 4 - 3 + 3 = 0 + 3
x / 4 = 3
Multiply both sides by 4
x = 4 ∙ 3
x = 12
x = 12 , y = - 3