Question

10x−9y=
−32
2, x, minus, 10, y, equals, 10
2x−10y=
10
Answer
Attempt 1 out of 5

left parenthesis(
,
right parenthesis)

Answer 1

To solve the system of equations:

1. \( 10x - 9y = -32 \) (Equation 1)
2. \( 2x - 10y = 10 \) (Equation 2)

We can solve this system using the substitution or elimination method. Let's use the elimination method.

First, we'll rearrange both equations to make elimination straightforward.

From Equation 2, we can isolate \( y \):

\[ 2x - 10y = 10 \]

Rearranging gives us:

\[ -10y = 10 - 2x \]

So,

\[ y = \frac{2x - 10}{10} \]

Now we will substitute \( y \) in Equation 1:

Replacing \( y \) in Equation 1:

\[ 10x - 9\left(\frac{2x - 10}{10}\right) = -32 \]

Multiply everything by 10 to eliminate the fraction:

\[ 100x - 9(2x - 10) = -320 \]

Distributing gives:

\[ 100x - 18x + 90 = -320 \]

Combining like terms:

\[ 82x + 90 = -320 \]

Subtracting 90 from both sides:

\[ 82x = -410 \]

Now dividing by 82:

\[ x = \frac{-410}{82} = -5 \]

Now that we have \( x \), we can substitute back to find \( y \). Using \( x = -5 \) in Equation 2:

\[ 2(-5) - 10y = 10 \]

Which simplifies to:

\[ -10 - 10y = 10 \]

Adding 10 to both sides gives:

\[ -10y = 20 \]

Dividing by -10 gives:

\[ y = -2 \]

Thus, the solution to the system of equations is \( (x, y) = (-5, -2) \).

So the final answer is:
\[
(-5, -2)
\]