Question

solve the following system of equations for all three variables.
-2x + 3y + 4z = 5
6x + 7y + z = 9
3x + 7y + z = -9
answer attempt 2 out of 2
x =
y =
z =
submit answer

Explanation:

Step1: Subtract the third equation from the second

Subtract $3x + 7y+z=-9$ from $6x + 7y + z = 9$.
$$(6x + 7y + z)-(3x + 7y + z)=9-(-9)$$
$$6x + 7y + z - 3x - 7y - z=9 + 9$$
$$3x=18$$
$$x = 6$$

Step2: Substitute $x = 6$ into the first and second equations

First equation: $-2\times6+3y + 4z=5$, which simplifies to $-12+3y + 4z=5$, or $3y+4z=17$.
Second equation: $6\times6 + 7y+z=9$, which simplifies to $36+7y + z=9$, or $7y+z=-27$. Then $z=-27 - 7y$.

Step3: Substitute $z=-27 - 7y$ into $3y+4z=17$

$3y+4(-27 - 7y)=17$.
$3y-108-28y=17$.
$-25y=17 + 108$.
$-25y=125$.
$y=-5$.

Step4: Substitute $y = - 5$ into $z=-27 - 7y$

$z=-27-7\times(-5)$.
$z=-27 + 35$.
$z = 8$.

Answer:

$x = 6$, $y=-5$, $z = 8$