Math  /  Algebra

Questionx=46x10y=6\begin{array}{l}x=-4 \\ 6 x-10 y=6\end{array}

Studdy Solution

STEP 1

What is this asking? We're given x=4x = -4 and asked to find yy using the equation 6x10y=66x - 10y = 6.
Basically, plug in xx and solve for yy! Watch out! Don't forget your negative signs when substituting and simplifying!

STEP 2

1. Substitute
2. Isolate and Solve

STEP 3

Alright, let's **kick things off** by plugging in our **known value** x=4x = -4 into our **main equation**: 6x10y=66x - 10y = 6.
This gives us 6(4)10y=66 \cdot (-4) - 10y = 6.

STEP 4

Now, let's **simplify**! 6(4)6 \cdot (-4) gives us 24-24.
So, our equation becomes 2410y=6-24 - 10y = 6.

STEP 5

We want that yy **all by itself**!
To do this, let's **add** 2424 to **both sides** of the equation: 2410y+24=6+24-24 - 10y + 24 = 6 + 24.
This simplifies to 10y=30-10y = 30.
Remember, we're adding 2424 to **zero out** the 24-24 on the left side.

STEP 6

Almost there!
Now, we just need to **divide both sides** of the equation by 10-10.
So, we have 10y10=3010\frac{-10y}{-10} = \frac{30}{-10}.
This gives us our **final answer**: y=3y = -3.
We're dividing by 10-10 to **scale** the 10y-10y down to 1y1y, which is just yy.

STEP 7

We found y=3y = -3 when x=4x = -4.

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