Question

1. reasoning suni needs to solve the system of equations using elimination.

$-5x + 3y = 15$
$2x - 3y = -15$
a. what variable should suni solve for first? explain.
b. find the solution.

Explanation:

Step1: Identify eliminable variable

The coefficients of $y$ are $3$ and $-3$, which are additive inverses. Adding the equations will eliminate $y$ directly, so $y$ should be solved for first (by elimination).

Step2: Add the two equations

$$(-5x + 3y) + (2x - 3y) = 15 + (-15)$$
Simplify:
$$-3x = 0$$

Step3: Solve for $x$

$$x = \frac{0}{-3} = 0$$

Step4: Substitute $x=0$ into first equation

$$-5(0) + 3y = 15$$
Simplify:
$$3y = 15$$

Step5: Solve for $y$

$$y = \frac{15}{3} = 5$$

Answer:

a. Suni should solve for $y$ first. The coefficients of $y$ ($3$ and $-3$) are additive inverses, so adding the two equations will eliminate $y$ immediately, making it the easiest variable to eliminate first.
b. The solution to the system is $x=0$, $y=5$ (or written as the ordered pair $(0, 5)$)