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

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

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Answer 1 · 2016-07-30T15:48:42

$x = \frac{3}{5}$ $x=3/5$
$y = \frac{19}{5}$ $y=19/5$

Explanation:

$2 x + y = 5$ $2x+y=5$
Putting $y = 3 x + 2$ $y=3x+2$ in the above equation we get
$2 x + 3 x + 2 = 5$ $2x+3x+2=5$
or
$5 x + 2 = 5$ $5x+2=5$
or
$5 x = 5 - 2$ $5x=5-2$
or
$5 x = 3$ $5x=3$
or
$x = \frac{3}{5}$ $x=3/5$ =======Ans $1$ $1$
By putting $x = \frac{3}{5}$ $x=3/5$ in the equation $y = 3 x + 2$ $y=3x+2$
we get
$y = 3 (\frac{3}{5}) + 2$ $y=3(3/5)+2$
or
$y = \frac{9}{5} + 2$ $y=9/5+2$
or
$y = \frac{9 + 2 (5)}{5}$ $y=(9+2(5))/5$
or
$y = \frac{9 + 10}{5}$ $y=(9+10)/5$
or
$y = \frac{19}{5}$ $y=19/5$ =====Ans $2$ $2$

Answer 2 · 2016-07-30T15:59:43

$x = \frac{3}{5}, y = 3 \frac{4}{5}$ $x = 3/5, y = 3 4/5$

Explanation:

This type of question is particularly common when working with straight lines.

Note that there is a single $y$ $y$ term in both equations.

$y = - 2 x + 5 and y = 3 x + 2$ $y = -2x+5" and " y = 3x +2$

At the point where the two lines intersect, the $x - and y -$ $x- and y-$ values are equal.

If $y = y$ $" y = y" "$ it follows that:

$3 x + 2 = - 2 x + 5$ $3x +2 =-2x+5$

$5 x = 3$ $5x = 3$

$x = \frac{3}{5}$ $x = 3/5$

There are now two equations to find a value for y. If we get the same answer for each we will know our answers are correct.

$y = 3 \times \frac{3}{5} + 2 = 3 \frac{4}{5} y = - 2 \times \frac{3}{5} + 5 = 3 \frac{4}{5}$ $y = 3xx 3/5 +2 = 3 4/5" "y = -2 xx3/5 +5 = 3 4/5$

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

2 Answers

Explanation:

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