Math  /  Algebra

Question5x+5y=35 x+5 y=3
1 of 2: Determine the missing coordinate in the ordered pair (5,?)(-5, ?) so that it will satisfy the given equation.
How to enter your answer (opens in new window) 2 Points (5,(-5, \square

Studdy Solution

STEP 1

What is this asking? We need to find the value of yy when x=5x = -5 in the equation 5x+5y=35x + 5y = 3. Watch out! Don't forget that xx is **negative five**, not just five!
Also, make sure to follow the order of operations carefully.

STEP 2

1. Substitute and Simplify
2. Isolate and Solve

STEP 3

Let's **substitute** our value x=5x = -5 into the equation 5x+5y=35x + 5y = 3.
This gives us 5(5)+5y=35 \cdot (-5) + 5y = 3.
We're doing this to get an equation with only one unknown, yy, which we can then solve!

STEP 4

Now, let's **simplify** 5(5)5 \cdot (-5) to get 25-25.
So, our equation becomes 25+5y=3-25 + 5y = 3.
Remember, multiplying a positive number by a negative number results in a negative number.

STEP 5

To **isolate** the yy term, we need to get rid of the 25-25 on the left side.
We can do this by **adding** 2525 to *both* sides of the equation.
This keeps the equation balanced!
So, 25+5y+25=3+25-25 + 5y + 25 = 3 + 25.
Simplifying this gives us 5y=285y = 28.

STEP 6

Finally, to **solve** for yy, we need to **divide** both sides of the equation 5y=285y = 28 by 55.
This gives us 5y5=285\frac{5y}{5} = \frac{28}{5}.
Simplifying, we get y=285y = \frac{28}{5}.
We divided by 55 to turn the 55 multiplying yy into a 11, since 5/5=15/5 = 1.

STEP 7

So, the missing coordinate is 285\frac{28}{5}.
The ordered pair is (5,285)(-5, \frac{28}{5}).
We found the value of yy that satisfies the given equation when x=5x = -5!

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