Question

$4x + 3y - z = 10$
$8x + 7y - z = 6$
$6x + y + z = 4$
answer attempt 1 out of 2
$x = \square$ $y = \square$ $z = \square$
submit answer

Explanation:

Step1: Label the equations

Let:
$4x + 3y - z = 10 \quad (1)$
$8x + 7y - z = 6 \quad (2)$
$6x + y + z = 4 \quad (3)$

Step2: Eliminate $z$ with (1)-(2)

Subtract equation (1) from (2) to remove $z$:
$$(8x + 7y - z) - (4x + 3y - z) = 6 - 10$$
$$4x + 4y = -4$$
Simplify to: $x + y = -1 \quad (4)$

Step3: Eliminate $z$ with (1)+(3)

Add equation (1) and (3) to remove $z$:
$$(4x + 3y - z) + (6x + y + z) = 10 + 4$$
$$10x + 4y = 14$$
Simplify to: $5x + 2y = 7 \quad (5)$

Step4: Solve for $x$ using (4),(5)

From (4): $y = -1 - x$. Substitute into (5):
$$5x + 2(-1 - x) = 7$$
$$5x - 2 - 2x = 7$$
$$3x = 9$$
$$x = 3$$

Step5: Solve for $y$ using (4)

Substitute $x=3$ into (4):
$$3 + y = -1$$
$$y = -4$$

Step6: Solve for $z$ using (3)

Substitute $x=3, y=-4$ into (3):
$$6(3) + (-4) + z = 4$$
$$18 - 4 + z = 4$$
$$14 + z = 4$$
$$z = -10$$

Answer:

$x = 3$, $y = -4$, $z = -10$