Question

Find the solution of the system of equations.

2x + 5y = –11
-8x – 5y = -1
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Answer 1

x=-6

Explanation:

Answer 2

The solution to the system of equations is
`\(x = 2\)` and
`\(y = -3\)`.

To find the solution of the system of equations, you can use the method of elimination. Add the two equations to eliminate the \(y\)-terms:

`\[ (2x + 5y) + (-8x - 5y) = -11 + (-1) \]`

Combine like terms:

`\[ -6x = -12 \]`

Now, solve for \(x\):

`\[ x = (-12)/(-6) = 2 \]`

Now that you have the value of \(x\), substitute it back into one of the original equations to solve for \(y\). Let's use the first equation:

`\[ 2x + 5y = -11 \]`

`\[ 2(2) + 5y = -11 \]`

`\[ 4 + 5y = -11 \]`

Subtract 4 from both sides:

`\[ 5y = -15 \]`

Divide by 5:

`\[ y = -3 \]`

So, the solution to the system of equations is
`\(x = 2\)` and
`\(y = -3\)`.