Question

linear systems in 3 variables (level 1)
score: 0/1 penalty: none
question
solve the following system of equations for all three variables.
$-6x - 2y - 5z = 2$
$-3x + 2y + 6z = 5$
$10x - 2y - 7z = -10$
answer attempt 1 out of 2
$x = \square$ $y = \square$ $z = \square$ submit answer

Explanation:

Step1: Add Eq1 and Eq2 to eliminate $y$

$$(-6x - 2y - 5z) + (-3x + 2y + 6z) = 2 + 5$$
$$-9x + z = 7 \quad \text{(Eq4)}$$

Step2: Add Eq2 and Eq3 to eliminate $y$

$$(-3x + 2y + 6z) + (10x - 2y - 7z) = 5 + (-10)$$
$$7x - z = -5 \quad \text{(Eq5)}$$

Step3: Add Eq4 and Eq5 to solve $x$

$$(-9x + z) + (7x - z) = 7 + (-5)$$
$$-2x = 2$$
$$x = -1$$

Step4: Substitute $x=-1$ into Eq4

$$-9(-1) + z = 7$$
$$9 + z = 7$$
$$z = 7 - 9 = -2$$

Step5: Substitute $x=-1,z=-2$ into Eq2

$$-3(-1) + 2y + 6(-2) = 5$$
$$3 + 2y - 12 = 5$$
$$2y - 9 = 5$$
$$2y = 14$$
$$y = 7$$

Answer:

$x=-1$, $y=7$, $z=-2$