Question

what a hot streak, a 1 week streak and counting! fantastic consistency. you might need: calculator solve the system of equations. 10y + 7x = 29 -5y - 9x = 2 x = y = show calculator

Explanation:

Step1: Eliminate $y$ via scaling

Multiply the second equation by 2:
$$2(-5y - 9x) = 2(2) \implies -10y - 18x = 4$$

Step2: Add to first equation

Add the new equation to $10y + 7x = 29$:
$$(10y + 7x) + (-10y - 18x) = 29 + 4$$
$$-11x = 33$$

Step3: Solve for $x$

Divide both sides by $-11$:
$$x = \frac{33}{-11} = -3$$

Step4: Substitute $x=-3$ to find $y$

Plug $x=-3$ into $-5y -9x = 2$:
$$-5y -9(-3) = 2 \implies -5y +27 = 2$$
$$-5y = 2 -27 = -25$$
$$y = \frac{-25}{-5} = 5$$

Answer:

$x = -3$
$y = 5$