Rewrite the equation so that y is the ntion of x:
a. 1/7(49-7y)=5x-3y+14
b. 4(2x-3y)=-5(x+3y)
Can you please explain and show how to do these two problems? Thank you.
Combine terms and put y alone on one side of the equation.
4(2x-3y)=-5(x+3y)
8x - 12y = -5x - 15y
Add 15y and subtract 8x from both sides.
3y = -13x
y = -13x/3
Do a similar process with the first equation.
I hope this helps. Thanks for asking.
Thanks a lot!
For b, it also says "use the result to find y when x=-1, 0, 2."
Can you please check this?
f(-1)=y=13/3
f(0)=y=0/3
f(1)=y=-13/3
Thanks again!
The last one should say:
f(2)=y=-26/3
a. To rewrite the equation so that y is the function of x, we need to isolate the y variable on one side of the equation.
1/7(49 - 7y) = 5x - 3y + 14
First, distribute the 1/7 to the terms inside the parentheses:
49/7 - (1/7)(7y) = 5x - 3y + 14
Now, simplify the equation:
7 - y = 5x - 3y + 14
Next, bring the y terms to one side and the constant terms to the other side:
-y + 3y = 5x - 7 + 14
Combine the y terms and the constant terms:
2y = 5x + 7
Lastly, to get y as the function of x, divide both sides of the equation by 2:
y = (5/2)x + 7/2
So, the rewritten equation in terms of y as the function of x is y = (5/2)x + 7/2.
b. To rewrite the equation so that y is the function of x, follow a similar process as in part a:
4(2x - 3y) = -5(x + 3y)
First, distribute the 4 on the left side and the -5 on the right side:
8x - 12y = -5x - 15y
Next, bring all the y terms to one side and all the x terms to the other side:
8x + 5x = -15y + 12y
Combine the x terms and the y terms:
13x = -3y
Lastly, to get y as the function of x, divide both sides of the equation by -3:
y = -(13/3)x
So, the rewritten equation in terms of y as the function of x is y = -(13/3)x.