Question

2b. solve the system of equations.\

$$\begin{cases}10x + 3y = -42\\\\10x - 7y = -2\\end{cases}$$

\bigcirc infinitely many solutions (same line)\bigcirc (4, 3)\bigcirc (-3, -4)\bigcirc no solution (parallel lines)\bigcirc (3, 4)\bigcirc (-4, -3)

Explanation:

Step1: Subtract equations to eliminate $x$

$$(10x + 3y) - (10x - 7y) = -42 - (-2)$$
$$10x + 3y -10x +7y = -42 +2$$
$$10y = -40$$

Step2: Solve for $y$

$$y = \frac{-40}{10} = -4$$

Step3: Substitute $y=-4$ into second equation

$$10x -7(-4) = -2$$
$$10x +28 = -2$$

Step4: Solve for $x$

$$10x = -2 -28$$
$$10x = -30$$
$$x = \frac{-30}{10} = -3$$

Answer:

(-3, -4)