Question

−5x−y=9 and 3x−5y=17.

Answer 1

`\sf x = -1`

`\sf y = -4`

Explanation:

To solve the system of linear equations:

`\sf \begin{cases} -5x - y = 9 \\ 3x - 5y = 17 \end{cases}`

We can use the method of substitution or elimination. Let's use the substitution method.

Solve the first equation for one variable:

From the first equation, solve for
`\sf y`:

`\sf -5x - y = 9`

`\sf -y = 5x + 9`

`\sf y = -5x - 9`

Substitute the expression into the second equation:

Substitute
`\sf -5x - 9` for
`\sf y` in the second equation:

`\sf 3x - 5(-5x - 9) = 17`

Solve for
`\sf x`:

Solve the equation obtained in step 2 for
`\sf x`:

`\sf 3x + 25x + 45 = 17`

`\sf 28x = -28`

`\sf (28x)/(28)=(-28)/(28)`

`\sf x = -1`

Substitute the value of
`\sf x` back into one of the original equations to solve for
`\sf y`:

Use the first equation:

`\sf -5(-1) - y = 9`

`\sf 5 - y = 9`

`\sf y = 5-9`

`\sf y = -4`

So, the solution to the system of equations is
`\sf x = -1` and
`\sf y = -4`.