How do you solve the system of equations by graphing $8 x + 5 y = - 3$ $8x + 5y = -3$ and $- 2 x + y = 21$ $-2x + y = 21$ and then classify the system?

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How do you solve the system of equations by graphing $8 x + 5 y = - 3$ $8x + 5y = -3$ and $- 2 x + y = 21$ $-2x + y = 21$ and then classify the system?

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Answer 1 · 2018-06-04T15:13:43

$x = - 6$ $x = -6$
$y = 9$ $y = 9$

Explanation:

$8 x + 5 y = - 3$ $8x + 5y = -3$
$- 2 x + y = 21$ $-2x + y = 21$

Solving by Substitution

First, we're going to find an equation for the value of a variable to plug it into the other equation in the system. $- 2 x + y = 21$ $-2x + y = 21$ looks like it can easily be rearranged to get the equation for the value of $y$ $y$ .

$- 2 x + y = 21$ $-2x + y = 21$

Add $2 x$ $2x$ to both sides to isolate for the equation for the value of $y$ $y$ . You should now have:

$y = 2 x + 21$ $y = 2x + 21$

Now that you have the equation for the value of $y$ $y$ , you can plug the terms $(2 x + 21)$ $(2x + 21)$ into where $y$ $y$ would appear in the other equation of the system. So:

$8 x + 5 y = - 3$ $8x + 5y = -3$
$8 x + 5 (2 x + 21) = - 3$ $8x + 5(2x + 21) = -3$

Distribute. What this means is that you'll be multiplying $2 x$ $2x$ by $5$ $5$ and $21$ $21$ by $5$ $5$ . So:

$5 \cdot 2 x = 10 x$ $5 * 2x = 10x$
$5 \cdot 21 = 105$ $5 * 21 = 105$

Re-write the equation:

$8 x + 10 x + 105 = - 3$ $8x + 10x + 105 = -3$
Combine like terms $(10 x + 8 = 18 x)$ $(10x + 8 = 18x)$ :

$18 x + 105 = - 3$ $18x + 105 = -3$

This is a two-step equation. Subtract $105$ $105$ from both sides to cancel out $105$ $105$ in order to get closer to finding the value of $x$ $x$ .

$18 x = - 108$ $18x = -108$

Divide by $18$ $18$ to isolate for $x$ $x$ :

$- \frac{108}{18} = x$ $-108/18 = x$

$- \frac{108}{18} = - 6$ $-108/18 = -6$

$x = - 6$ $x = -6$

Plug the value of $x$ $x$ back into the equation for the value of $y$ $y$ to figure out $y$ $y$ 's value:

$y = 2 x + 21$ $y = 2x + 21$
$y = 2 (- 6) + 21$ $y = 2(-6) + 21$
$y = - 12 + 21$ $y = -12 + 21$
$y = 9$ $y = 9$

Plug these values back into the whole system to prove they're right:

$8 x + 5 y = - 3$ $8x + 5y = -3$
$8 (- 6) + 5 (9) = - 3$ $8(-6) + 5(9) = -3$
$- 48 + 45 = - 3$ $-48 + 45 = -3$
$- 3 = - 3$ $-3 = -3$

$- 2 x + y = 21$ $-2x + y = 21$
$- 2 (- 6) + 9 = 21$ $-2(-6) + 9 = 21$
$12 + 9 = 21$ $12 + 9 = 21$
$21 = 21$ $21 = 21$

These are the correct values.

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How do you solve the system of equations by graphing $8 x + 5 y = - 3$ $8x + 5y = -3$ and $- 2 x + y = 21$ $-2x + y = 21$ and then classify the system?

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Explanation:

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How do you solve the system of equations by graphing $8 x + 5 y = - 3$ $8x + 5y = -3$ and $- 2 x + y = 21$ $-2x + y = 21$ and then classify the system?