$$ \begin{array}{l} ext { Solve the following system of equations. }\ \begin{aligned} 2 x-5 y & =4 \ -2 x+10 y & =-14 \end{aligned}\ x=\ y= \end{array} $$

Question

$$ \begin{array}{l} 	ext { Solve the following system of equations. }\ \begin{aligned} 2 x-5 y & =4 \ -2 x+10 y & =-14 \end{aligned}\ x=\ y= \end{array} $$

UpStudy AI · Accepted Answer

1. Start with the system of equations:
   $$
   \begin{aligned}
   2x - 5y &= 4 \quad \text{(1)} \
   -2x + 10y &= -14 \quad \text{(2)}
   \end{aligned}
   $$

2. Add equations (1) and (2) to eliminate $$x$$:
   $$
   (2x - 5y) + (-2x + 10y) = 4 + (-14)
   $$
   Simplify:
   $$
   0x + 5y = -10
   $$
   Therefore,
   $$
   5y = -10 \quad \Rightarrow \quad y = \frac{-10}{5} = -2
   $$

3. Substitute $$y = -2$$ into equation (1) to solve for $$x$$:
   $$
   2x - 5(-2) = 4
   $$
   Simplify:
   $$
   2x + 10 = 4
   $$
   Solve for $$x$$:
   $$
   2x = 4 - 10 = -6 \quad \Rightarrow \quad x = \frac{-6}{2} = -3
   $$

4. The solution to the system is:
   $$
   x = -3, \quad y = -2
   $$
$$ x = -3 $$, $$ y = -2 $$

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