Answer:
x = 31/32 and y = 15/8.
Explanation:
The given equation is 4x - 2y = 1.
To solve this equation using the substitution method, we need to solve one of the equations for one variable and then substitute that expression into the other equation.
Let's solve the given equation for x:
4x - 2y = 1
First, we isolate x by subtracting 2y from both sides of the equation:
4x = 2y + 1
Then, we divide both sides of the equation by 4 to solve for x:
x = (2y + 1)/4
Now that we have solved for x, we can substitute this expression into the other equation.
Let's assume we have another equation, for example, 2x + 3y = 8.
Substituting x = (2y + 1)/4 into this equation, we get:
2((2y + 1)/4) + 3y = 8
Simplifying this equation, we get:
(2y + 1)/2 + 3y = 8
Multiplying both sides of the equation by 2 to clear the fraction, we get:
2y + 1 + 6y = 16
Combining like terms, we have:
8y + 1 = 16
Subtracting 1 from both sides of the equation, we get:
8y = 15
Dividing both sides of the equation by 8, we get:
y = 15/8
Now that we have solved for y, we can substitute this value back into x = (2y + 1)/4 to find the value of x.
Using y = 15/8, we have:
x = (2(15/8) + 1)/4
Simplifying this expression, we get:
x = (30/8 + 1)/4
Adding the fractions, we have:
x = (31/8)/4
Dividing the fractions, we get:
x = 31/32
Therefore, the solution to the equation 4x - 2y = 1 is x = 31/32 and y = 15/8.