# How do you solve the system using the elimination method for 3/2x - 2/3y =3 and 1/2x - 1/4y= -1?

Jul 15, 2015

I found:
$x = 34$
$y = 72$

#### Explanation:

I would multiply the second equation by $- 3$ to get:
{3/2x-2/3y=3
{color(red)(-3/2x+3/4y=3)
adding the two equations (in columns) you get:
$0 - \frac{2}{3} y + \frac{3}{4} y = 6$
$\frac{- 8 y + 9 y}{12} = 6$ and rearranging:
$y = 6 \cdot 12 = 72$
substituting back $y = 72$ into the first equation you get:
$\frac{3}{2} x - \frac{2}{3} \cdot 72 = 3$
$\frac{3}{2} x - 48 = 3$
$\frac{3}{2} x = 51$
and $x = 34$
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 13, "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, "url": "https://socratic.org/questions/how-do-you-solve-the-system-using-the-elimination-method-for-3-2x-2-3y-3-and-1-2", "fetch_time": 1576463350000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2019-51/segments/1575541315293.87/warc/CC-MAIN-20191216013805-20191216041805-00232.warc.gz", "warc_record_offset": 556950401, "warc_record_length": 6273, "token_count": 256, "char_count": 570, "score": 4.34375, "int_score": 4, "crawl": "CC-MAIN-2019-51", "snapshot_type": "longest", "language": "en", "language_score": 0.700756311416626, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00017-of-00064.parquet"}