Answer:
To solve the system of equations using the cross multiplication method, we can follow these steps:
Step 1: Rearrange the equations in the form of "ax + by = c".
Given equations:
3x - 4y = 1 ...(Equation 1)
2y - x = 1 ...(Equation 2)
Step 2: Multiply Equation 1 by the coefficient of y in Equation 2, and multiply Equation 2 by the coefficient of y in Equation 1.
Multiply Equation 1 by 2:
6x - 8y = 2 ...(Equation 3)
Multiply Equation 2 by 3:
6y - 3x = 3 ...(Equation 4)
Step 3: Subtract Equation 4 from Equation 3 to eliminate the variable y.
(6x - 8y) - (6y - 3x) = 2 - 3
Simplifying the equation:
6x - 8y - 6y + 3x = -1
Combine like terms:
9x - 14y = -1 ...(Equation 5)
Step 4: Solve Equation 5 for one variable (x or y).
9x - 14y = -1
Let's solve for x:
9x = 14y - 1
x = (14y - 1)/9 ...(Equation 6)
Step 5: Substitute the value of x from Equation 6 into either Equation 1 or Equation 2 to solve for the other variable.
Substitute x = (14y - 1)/9 into Equation 1:
3((14y - 1)/9) - 4y = 1
Simplify the equation:
(42y - 3)/9 - 4y = 1
Multiply through by 9 to eliminate the fraction:
42y - 3 - 36y = 9
6y - 3 = 9
Add 3 to both sides:
6y = 12
Divide by 6:
y = 2
Step 6: Substitute the value of y = 2 into Equation 6 to find the value of x.
x = (14(2) - 1)/9
x = 27/9
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 2.
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Answer:
To solve the system of equations using the cross multiplication method, we can follow these steps:
Step 1: Rearrange the equations in the form of "ax + by = c".
Given equations:
3x - 4y = 1 ...(Equation 1)
2y - x = 1 ...(Equation 2)
Step 2: Multiply Equation 1 by the coefficient of y in Equation 2, and multiply Equation 2 by the coefficient of y in Equation 1.
Multiply Equation 1 by 2:
6x - 8y = 2 ...(Equation 3)
Multiply Equation 2 by 3:
6y - 3x = 3 ...(Equation 4)
Step 3: Subtract Equation 4 from Equation 3 to eliminate the variable y.
(6x - 8y) - (6y - 3x) = 2 - 3
Simplifying the equation:
6x - 8y - 6y + 3x = -1
Combine like terms:
9x - 14y = -1 ...(Equation 5)
Step 4: Solve Equation 5 for one variable (x or y).
9x - 14y = -1
Let's solve for x:
9x = 14y - 1
x = (14y - 1)/9 ...(Equation 6)
Step 5: Substitute the value of x from Equation 6 into either Equation 1 or Equation 2 to solve for the other variable.
Substitute x = (14y - 1)/9 into Equation 1:
3((14y - 1)/9) - 4y = 1
Simplify the equation:
(42y - 3)/9 - 4y = 1
Multiply through by 9 to eliminate the fraction:
42y - 3 - 36y = 9
Combine like terms:
6y - 3 = 9
Add 3 to both sides:
6y = 12
Divide by 6:
y = 2
Step 6: Substitute the value of y = 2 into Equation 6 to find the value of x.
x = (14(2) - 1)/9
x = 27/9
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 2.