For each equarion, write the equivalent equation that expresses y in terms of x
(Problem A)
3x+5x-y=5y
y=
(Problem B)
3x(5-x)= x-y
Get all the y terms on one side.
I will do B for you and let you do A.
First, get rid of the parenthesis.
15x-3x^2=x-y
Move the x and multiply by -1.
3x^2-14x=y
I hope this helps you to do the first problem. Thanks for asking.
8x^2=6y
To solve both Problem A and Problem B and express y in terms of x, we need to isolate y on one side of the equation. Let's solve each problem step by step.
Problem A:
3x + 5x - y = 5y
Let's collect similar terms:
8x - y = 5y
We'll move all the terms with y to the left side by adding y to both sides:
8x - y + y = 5y + y
Simplifying the equation gives us:
8x = 6y
Now to express y in terms of x, we can divide both sides of the equation by 6:
(8/6)x = (6/6)y
Simplifying further:
(4/3)x = y
Therefore, the equivalent equation expressing y in terms of x for Problem A is:
y = (4/3)x
Problem B:
3x(5 - x) = x - y
To begin, we'll simplify the left side of the equation by distributing the 3x:
15x - 3x^2 = x - y
Let's rearrange the terms:
-3x^2 + 15x = x - y
Moving the terms with y to the left side by adding y to both sides:
-3x^2 + 15x + y = x
Now, to express y in terms of x, we'll subtract x from both sides:
-3x^2 + 15x + y - x = 0
Simplifying the equation further yields:
-3x^2 + 14x + y = 0
Finally, we can express y in terms of x by subtracting -3x^2 and 14x from both sides:
y = 3x^2 - 14x
Therefore, the equivalent equation expressing y in terms of x for Problem B is:
y = 3x^2 - 14x