Question #1847b

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Question #1847b

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Answer 1 · 2015-10-02T05:52:13

First number is -10
Second number is -8

Explanation:

Let $x$ $x$ be the first number.
Let $y$ $y$ be the second number.

First Equation:
The first number is 2 less than the second number.
$x = y - 2$ $color(blue)(x=y-2)$

Second Equation:
Twice the first number is 4 more than 3 times the second.
$2 x = 4 + 3 y$ $color(red)(2x=4+3y)$

System:
$x = y - 2$ $color(blue)(x=y-2)$
$2 x = 4 + 3 y$ $color(red)(2x=4+3y)$

We can solve this by substitution. Let's get the value of $x$ $x$ in the first equation and substitute it into $x$ $x$ in the second equation. Then, we can solve for $y$ $y$ .

$2 x = 4 + 3 y$ $2color(blue)(x)=4+3y$
$2 (y - 2) = 4 + 3 y$ $2color(blue)((y-2))=4+3y$
$2 y - 4 = 4 + 3 y$ $2y-4=4+3y$
$2 y - 4 - 3 y = 4 + 3 y - 3 y$ $2y-4-3y=4+3y-3y$
$- 4 - y = 4$ $-4-y=4$
$- 4 - y + 4 = 4 + 4$ $-4-y+4=4+4$
$- y = 8$ $-y=8$
$y = - 8$ $color(magenta)(y=-8)$

To solve for $x$ $x$ , just substitute the value of $y$ $y$ into either of the two equations.
$x = y - 2$ $x=color(magenta)(y)-2$
$x = (- 8) - 2$ $x=color(magenta)((-8))-2$
$x = - 10$ $color(orange)(x=-10)$

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Question #1847b

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