Question

1. critique the reasoning of others. kyla was asked to solve the system of equations below. she made the graph shown and stated that the solution of the system is (-4, -1). is kyla correct? justify your response and identify kyla’s errors, if they exist. x + y = 3 x - 3y = -1

Explanation:

Step1: Solve the system algebraically

First, use substitution or elimination. Let's use substitution. From $x + y = 3$, rearrange to $x = 3 - y$. Substitute into the second equation:
$$(3 - y) - 3y = -1$$

Step2: Simplify and solve for y

Combine like terms:
$$3 - 4y = -1$$
Subtract 3 from both sides:
$$-4y = -4$$
Divide by -4:
$$y = 1$$

Step3: Solve for x

Substitute $y=1$ into $x = 3 - y$:
$$x = 3 - 1 = 2$$

Step4: Check Kyla's point

Test $(-4, -1)$ in the first equation:

$$-4 + (-1) = -5 eq 3$$

Test in the second equation:
$$-4 - 3(-1) = -4 + 3 = -1$$
The point only satisfies one equation, not both. Also, the graph shows the lines intersecting at $(-4, -1)$, but this is incorrect because the lines graphed do not match the given equations.

Answer:

Kyla is not correct. The actual solution to the system is $(2, 1)$, as this point satisfies both equations: $2 + 1 = 3$ and $2 - 3(1) = -1$. Kyla's error is that the lines she graphed do not correspond to the given equations, and her proposed solution $(-4, -1)$ only satisfies the second equation, not the first.