Question

-2x - 5y = -5\
-3x - 10y = -20\
(\boxed{ }, \boxed{ })\
submit

Explanation:

Step1: Analyze the system of equations

We have the system:

$$
LATEXBLOCK0
$$

Let's use the elimination method. First, multiply the first equation by 2 to make the coefficients of \(y\) opposite:

$$ -4x - 10y = -10 $$

Step2: Subtract the second equation

Now subtract the second equation \(-3x - 10y = -20\) from the new first equation:

$$ (-4x - 10y) - (-3x - 10y) = -10 - (-20) $$

Simplify the left side:

$$ -4x - 10y + 3x + 10y = -10 + 20 $$

$$ -x = 10 $$

So \(x = -10\)

Step3: Substitute \(x\) into the first equation

Substitute \(x = -10\) into \(-2x - 5y = -5\):

$$ -2(-10) - 5y = -5 $$

$$ 20 - 5y = -5 $$

Subtract 20 from both sides:

$$ -5y = -5 - 20 $$

$$ -5y = -25 $$

Divide both sides by -5:

$$ y = 5 $$

Answer:

The solution to the system of equations is \(x = -10\) and \(y = 5\). If we assume the boxes are for the solution of the system (maybe in the form of \((x,y)\)), then the answer is \((-10, 5)\)