Explanation:
o find the values of x and y in the equation x + 3y = 15, we can use algebraic methods.
Step 1: Start by rearranging the equation to isolate one variable. Let's isolate x by subtracting 3y from both sides of the equation:
x + 3y - 3y = 15 - 3y
This simplifies to:
x = 15 - 3y
Step 2: Now we have an expression for x in terms of y. We can substitute this expression into the original equation to solve for y.
Substituting x = 15 - 3y into the equation x + 3y = 15:
(15 - 3y) + 3y = 15
Step 3: Simplify and solve for y.
15 - 3y + 3y = 15
The -3y and +3y cancel each other out, leaving us with:
15 = 15
Step 4: Since 15 is equal to 15, this means that y can be any value. Therefore, there are infinitely many solutions for y.
Step 5: To find the corresponding values of x, we can substitute the value of y back into the expression x = 15 - 3y.
For example, if we choose y = 0, then:
x = 15 - 3(0)
x = 15
So, when y = 0, x = 15.
Similarly, if we choose y = 2, then:
x = 15 - 3(2)
x = 9
So, when y = 2, x = 9.
In summary, the values of x and y in the equation x + 3y = 15 can vary. For any chosen value of y, you can find the corresponding value of x using the expression x = 15 - 3y.
Hope this helps.