Question

The question is in the image

Please help connexus friends :)

Answer 1

The solution to the system of equations 5x + y = 0 and 5x + 2y = 30 is x = -6 and y = 30, obtained through substitution by solving for y and substituting the result.

To find the solution to the system using substitution or elimination, let's choose one method. I'll demonstrate using substitution.

Substitution:

1. Solve the first equation for one variable, say \(y\).

`\[ 5x + y = 0 \] \[ y = -5x \]`

2. Substitute this expression into the second equation.

`\[ 5x + 2y = 30 \] \[ 5x + 2(-5x) = 30 \]`

3. Simplify and solve for x.

`\[ 5x - 10x = 30 \] \[ -5x = 30 \] \[ x = -6 \]`

4. Substitute the value of x back into the expression for y.

`\[ y = -5(-6) \] \[ y = 30 \]`

So, the solution to the system is x = -6 and y = 30.