The system shows that you uploaded a photo with two equations to solve by the elimination method:

1. $x + y = -5$
2. $3x + 7y = -15$

To solve using the elimination method, the goal is to eliminate one variable by combining the equations. Here's how you can proceed:

Step 1: Multiply the first equation to align the coefficients of either $x$ or $y$ in both equations.

• Multiply the first equation by 3 (so the coefficient of $x$ becomes 3):

$3(x + y = -5) \implies 3x + 3y = -15$

Now you have the system: $3x + 3y = -15$ $3x + 7y = -15$

Step 2: Subtract the first equation from the second equation to eliminate $x$:

$(3x + 7y) - (3x + 3y) = -15 - (-15)$

This simplifies to:

$4y = 0$

Step 3: Solve for $y$:

$y = 0$

Step 4: Substitute $y = 0$ back into one of the original equations (e.g., the first one):

$x + 0 = -5$

Thus:

$x = -5$

Final solution:

$x = -5, \quad y = 0$

Would you like further clarification or details on the steps? Here are some related questions:

1. How do you use substitution to solve a system of equations?
2. What happens if the system has no solution?
3. How does the elimination method compare to the substitution method?
4. How do you deal with fractional coefficients when using elimination?
5. What if the variables cancel out during elimination—what does that mean for the system?

Tip: When using the elimination method, it’s helpful to first manipulate the coefficients of the variables to match each other. This makes eliminating one variable straightforward.