Question

solve the system using substitution
y = -4x - 8
-5x - 3y = 3
○ (-3, 4)
○ infinitely many solutions
○ (4, 3)
○ no solution

Explanation:

Step1: Substitute $y$ into second equation

Substitute $y=-4x-8$ into $-5x-3y=3$:
$$-5x - 3(-4x - 8) = 3$$

Step2: Expand and simplify the equation

$$-5x + 12x + 24 = 3$$
$$7x + 24 = 3$$

Step3: Isolate $x$ term

$$7x = 3 - 24$$
$$7x = -21$$

Step4: Solve for $x$

$$x = \frac{-21}{7} = -3$$

Step5: Solve for $y$

Substitute $x=-3$ into $y=-4x-8$:
$$y = -4(-3) - 8 = 12 - 8 = 4$$

Answer:

(-3, 4)