How do you solve $y = - x + 5$ $y = -x + 5$ and $2 x - 3 y = - 6$ $2x - 3y = -6$ using substitution?

Question

How do you solve $y = - x + 5$ $y = -x + 5$ and $2 x - 3 y = - 6$ $2x - 3y = -6$ using substitution?

1 Answer

Impact of this question

990 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-17T22:02:55

$(\frac{9}{5}, \frac{16}{5})$ $(9/5,16/5)$

Explanation:

As given by the first equation, we see that $y = - x + 5$ $color(red)(y=-x+5)$ . Because of this, we can plug $- x + 5$ $color(red)(-x+5$ in for $y$ $color(red)y$ in the second equation.

$2 x - 3 y = - 6 \Rightarrow 2 x - 3 (- x + 5) = - 6$ $2x-3color(red)y=-6" "=>" "2x-3(color(red)(-x+5))=-6$

When distributing $- 3$ $-3$ into $(- x + 5)$ $(-x+5)$ , note that the negative will change the signs of the terms in the parentheses, so:

$- 3 (- x + 5) = + 3 x - 15$ $-3(color(blue)-xcolor(blue)+5)=color(green)+3xcolor(green)-15$

So, we have

$2 x + 3 x - 15 = - 6$ $2x+3x-15=-6$

$5 x - 15 = - 6$ $5x-15=-6$

$5 x = 9$ $5x=9$

$x = \frac{9}{5}$ $color(purple)(x=9/5$

With this, we can plug this value for $x$ $x$ into either equation. I'll choose the first, since it's simpler:

$y = - x + 5 \Rightarrow y = - \frac{9}{5} + 5$ $y=-color(purple)x+5" "=>" "y=-color(purple)(9/5)+5$

Find a common denominator:

$y = - \frac{9}{5} + \frac{25}{5}$ $y=-9/5+25/5$

$y = \frac{16}{5}$ $color(brown)(y=16/5)$

Since we have $x = \frac{9}{5}$ $color(purple)(x=9/5$ and $y = \frac{16}{5}$ $color(brown)(y=16/5)$ , our final answer is the ordered pair $(\frac{9}{5}, \frac{16}{5})$ $(color(purple)(9/5),color(brown)(16/5))$ .

Science

Math

Humanities

... and beyond

How do you solve $y = - x + 5$ $y = -x + 5$ and $2 x - 3 y = - 6$ $2x - 3y = -6$ using substitution?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve y=−x+5y = -x + 5 and 2x−3y=−62x - 3y = -6 using substitution?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve $y = - x + 5$ $y = -x + 5$ and $2 x - 3 y = - 6$ $2x - 3y = -6$ using substitution?