Question

8x - 2y = 2 and - 3x + 2y = - 2

• 6x - 10y = 20 and - 9x - 10y =

Explanation:

Step1: Solve the first system of equations

We have the system:

$$
LATEXBLOCK0
$$

Add the two equations together to eliminate \(y\):

$$ (8x - 2y)+(-3x + 2y)=2+(-2) $$

$$ 8x - 2y-3x + 2y=0 $$

$$ 5x=0 $$

So \(x = 0\).
Substitute \(x = 0\) into the first equation \(8x-2y = 2\):

$$ 8(0)-2y=2 $$

$$ -2y=2 $$

$$ y=- 1 $$

Step2: Analyze the second system (incomplete, but we can note the structure)

The second system is given as \(-6x - 10y = 20\) and \(-9x - 10y=\) (incomplete). If we assume we want to solve it (once completed), we can use the elimination method similar to the first system. Since the coefficients of \(y\) are the same (\(- 10y\)), we can subtract the two equations (or add depending on the sign) to eliminate \(y\) and solve for \(x\), then substitute back to find \(y\).

Answer:

For the first system, the solution is \(x = 0\), \(y=-1\). The second system is incomplete, but the method to solve it (when completed) is similar to the first system (elimination by adding/subtracting to eliminate \(y\) since the coefficients of \(y\) are the same).