# How do you solve 3x+y=3 and 2x+3y=-5?

Sep 5, 2015

The solution is
color(blue)(x=2,y=-3

#### Explanation:

$3 x + y = 3$, multiplying the equation by $3$
$9 x + \textcolor{b l u e}{3 y} = 9$........equation $1$

$2 x + \textcolor{b l u e}{3 y} = - 5$....equation $2$

Solving by elimination as subtracting the two equations eliminates color(blue)(3y

Subtracting equation $2$ from $1$
$9 x + \cancel{\textcolor{b l u e}{3 y}} = 9$

$- 2 x - \cancel{\textcolor{b l u e}{3 y}} = + 5$

$7 x = 14$
color(blue)(x=2

Finding $y$ by substituting $x$ in equation $1$
$3 x + y = 3$
$y = 3 - 3 x$
$y = 3 - 3 \cdot 2$
$y = 3 - 6$
color(blue)(y=-3
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 22, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}