How do you find the solution of the system of equations y = 4-x^2 and 3x+y = 0?

May 10, 2015

Given
$\text{[1] } y = 4 - {x}^{2}$
$\text{[2] } 3 x + y = 0$

Rearranging $\text{[2]}$
$\text{[3] } y = - 3 x$

Substituting $\text{[3]}$ into $\text{[1]}$
$\text{[4] } - 3 x = 4 - {x}^{2}$

Rearranging $\text{[4]}$
$\text{[5] } {x}^{2} - 3 x - 4 = 0$

Factoring the left-hand side of $\text{[5]}$
$\text{[6] } \left(x - 4\right) \left(x + 1\right) = 0$

Solution:
$x = 4$ or $x = - 1$
{"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-find-the-solution-of-the-system-of-equations-y-4-x-2-and-3x-y-0", "fetch_time": 1716960617000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2024-22/segments/1715971059206.29/warc/CC-MAIN-20240529041915-20240529071915-00615.warc.gz", "warc_record_offset": 461548046, "warc_record_length": 6016, "token_count": 231, "char_count": 481, "score": 4.5, "int_score": 4, "crawl": "CC-MAIN-2024-22", "snapshot_type": "latest", "language": "en", "language_score": 0.5338675379753113, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00035-of-00064.parquet"}