solve for y and x
2x+4y=8 show steps
To solve for y and x in the equation 2x + 4y = 8, we will use the method of substitution. Here are the steps:
Step 1: Solve for y in terms of x
In order to eliminate one variable, we can solve one equation for one variable. Let's solve the given equation for y:
2x + 4y = 8
Subtract 2x from both sides:
4y = 8 - 2x
Divide both sides by 4:
y = (8 - 2x) / 4
y = 2 - 0.5x
Step 2: Substitute the value of y in the equation with the expression we obtained in step 1.
Now, we will substitute the expression for y back into the original equation to solve for x.
2x + 4y = 8
Substituting y = 2 - 0.5x:
2x + 4(2 - 0.5x) = 8
Step 3: Simplify and solve for x
Expand and simplify the equation:
2x + 8 - 2x = 8
The x variable cancels out, leaving us with:
8 = 8
Step 4: Analyze the solution
The equation 8 = 8 is true. This means that any value of x will satisfy the equation. In other words, the equation does not have a unique solution.
Step 5: Solve for y
Since the equation does not provide a unique value for x, we cannot find a specific value for y either. However, we can express y in terms of x using the original equation:
2x + 4y = 8
Solving for y:
4y = 8 - 2x
y = (8 - 2x) / 4
y = 2 - 0.5x
Therefore, the solution for the equation 2x + 4y = 8 is y = 2 - 0.5x, and it does not have a unique solution.