How do you solve the system of equations $7 x + 5 y + 7 z = 60$ $7x + 5y + 7z = 60$ , $15 x + 2 z = - 195$ $15x + 2z = - 195$ , and $5 z = 75$ $5z = 75$ ?

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How do you solve the system of equations $7 x + 5 y + 7 z = 60$ $7x + 5y + 7z = 60$ , $15 x + 2 z = - 195$ $15x + 2z = - 195$ , and $5 z = 75$ $5z = 75$ ?

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Answer 1 · 2018-08-06T21:29:43

$x = - 15$ $x=-15$
$y = 12$ $y=12$
$z = 15$ $z=15$

Explanation:

First solve for $z$ $z$ using the third equation

$z = \frac{75}{5} = 15$ $z=75/5=15$

Now that we know $z$ $z$ , we can plug it into the second equation and solve for $x$ $x$

$15 x + 2 (15) = - 195$ $15x+2(15)=-195$

$15 x = - 225$ $15x=-225$

$x = - 15$ $x=-15$

Now we can find $y$ $y$ using the values of $x$ $x$ and $z$ $z$ and plugging them into the first equation

$7 (- 15) + 5 y + 7 (15) = 60$ $7(-15)+5y+7(15)=60$

$5 y = 60$ $5y=60$

$y = 12$ $y=12$

Answer 2 · 2018-08-06T21:33:42

$x = - 15$ $x =-15$
$y = 12$ $y = 12$
$z = 15$ $z=15$

Explanation:

This question is far easier than it appears at first.

The key idea is that if a a linear equation has $1$ $1$ variable, there will be one solution, but as soon as there are $2$ $2$ variable, $2$ $2$ equations are required and likewise for $3$ $3$ variables, there must be $3$ $3$ equations.

We have all of these scenarios presented here.

Solve the $3 r d$ $3rd$ equation first as it only has $1$ $1$ variable,

$5 z = 75$ $5z = 75$
$z = 15 \leftarrow$ $color(blue)(z =15)" "larr$ now use this value for $z$ $z$ in the $2 n d$ $2nd$ equation:

$15 x + 2 z = - 195$ $15x +2color(blue)(z) = -195$
$15 x + 2 (15) = - 195$ $15x +2color(blue)((15)) = -195$
$15 x + 30 = - 195$ $15x +color(blue)(30) = -195$
$15 x = - 225$ $15x = -225$
$x = - 15 \leftarrow$ $color(green)(x =-15)" "larr$ use this value for $x$ $x$ in the first equation

$7 x + 5 y + 7 z = 60$ $7color(green)(x)+5y+7color(blue)(z)=60$
$7 (- 15) + 5 y + 7 (15) = 60$ $7color(green)((-15))+5y+7color(blue)((15))=60$

$- 105 + 5 y + 105 = 60$ $-105 +5y +105 = 60$
$5 y = 60$ $5y=60$
$y = 12$ $y=12$

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How do you solve the system of equations $7 x + 5 y + 7 z = 60$ $7x + 5y + 7z = 60$ , $15 x + 2 z = - 195$ $15x + 2z = - 195$ , and $5 z = 75$ $5z = 75$ ?

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How do you solve the system of equations 7x+5y+7z=607x + 5y + 7z = 60, 15x+2z=−19515x + 2z = - 195, and 5z=755z = 75?

2 Answers

Explanation:

Explanation:

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How do you solve the system of equations $7 x + 5 y + 7 z = 60$ $7x + 5y + 7z = 60$ , $15 x + 2 z = - 195$ $15x + 2z = - 195$ , and $5 z = 75$ $5z = 75$ ?