Today's HW, due tomorrow, I'm lost, please help.
1. 5y - 7x = 10
2. 2y = 10 - 2 (x - 3)
3. y = 2x + 1/2 (3x + 1) + 1/4 (2x + 8)
Of course! I'd be happy to help you with your homework. Let's work through each problem step-by-step together.
1. 5y - 7x = 10:
To solve this equation, we want to isolate the variable y. Start by moving the term with x to the other side of the equation by adding 7x to both sides:
5y = 7x + 10
Next, divide both sides of the equation by 5 to isolate y:
y = (7x + 10)/5
That's your solution for the first problem.
2. 2y = 10 - 2(x - 3):
We'll similarly work on isolating the variable y in this equation. First, distribute the -2 to both terms inside the parentheses, which gives:
2y = 10 - 2x + 6
Combine like terms:
2y = -2x + 16
Next, divide both sides by 2 to solve for y:
y = (-2x + 16)/2
Now, simplify the expression:
y = -x + 8
That's your answer for the second problem.
3. y = 2x + 1/2(3x + 1) + 1/4 (2x + 8):
To solve this equation, we need to follow the order of operations (PEMDAS/BODMAS). First, simplify the expression within the parentheses:
y = 2x + 1/2(3x + 1) + 1/4(2x + 8)
= 2x + 1/2 * 3x + 1/2 * 1 + 1/4 * 2x + 1/4 * 8
= 2x + 3/2x + 1/2 + 1/2x + 2
Combine like terms:
y = (2x + 3/2x + 1/2x) + (1/2 + 2)
= (7/2x) + (5/2)
So, the simplified equation is:
y = (7/2)x + (5/2)
That's your answer for the third problem.
Remember, it's important to check your answers by substituting them back into the original equations to make sure they satisfy the given equations. Let me know if you need any further assistance!