{"id":805,"date":"2023-05-07T16:49:29","date_gmt":"2023-05-07T16:49:29","guid":{"rendered":"http:\/\/yesrenee.com\/?p=805"},"modified":"2023-08-28T17:58:11","modified_gmt":"2023-08-28T17:58:11","slug":"how-to-solve-two-variable-equations","status":"publish","type":"post","link":"https:\/\/yesrenee.com\/?p=805","title":{"rendered":"How To Solve Two Variable Equations"},"content":{"rendered":"\n

There are a lot of situations where we find ourselves with two-variable equations, but it does seem frustrating trying to solve them. Here’s an example (where the answer is rounded to nearest integer):<\/p>\n\n\n\n

x<\/em> + 3y<\/em> = 7<\/p>\n\n\n\n

5x<\/em> – 2y<\/em> = 1<\/p>\n\n\n\n

There are two methods for solving this equation.<\/p>\n\n\n\n

Method 1:<\/p>\n\n\n\n

x<\/em> + 3y<\/em> = 7<\/p>\n\n\n\n

5x<\/em> – 2y<\/em> = 1<\/p>\n\n\n\n

We can first isolate a variable using one of the statements. You can pick any equation(such as eq. 1).<\/p>\n\n\n\n

x<\/em> + 3y<\/em> = 7 pick a variable(such as x)<\/em><\/p>\n\n\n\n

x<\/strong><\/em> + 3y<\/em> = 7<\/p>\n\n\n\n

x<\/strong><\/em> = 8 – 3y<\/em> isolate x<\/em><\/p>\n\n\n\n

5(8 – 3y<\/em>) – 2y<\/em> = 1 plug x into the second equation<\/em><\/p>\n\n\n\n

40 – 15y<\/em> – 2y<\/em> = 1 apply the distributive property <\/em><\/p>\n\n\n\n

40 – 17y<\/em> = 1 combine like terms<\/em><\/p>\n\n\n\n

-17y<\/em> = 1 – 40 step 1 of isolating y<\/em><\/p>\n\n\n\n

y<\/em> = -39\/-17 step 2 of isolating y<\/em><\/p>\n\n\n\n

y = 2<\/p>\n\n\n\n

Method 2:<\/p>\n\n\n\n

x<\/em> + 3y<\/em> = 7<\/p>\n\n\n\n

5x<\/em> – 2y<\/em> = 1<\/p>\n\n\n\n

We can cancel out one of the variables by merging both equations. To cancel one of them out, we need to multiply both eq.s.<\/p>\n\n\n\n

x<\/em> + 3y<\/em> = 7 multiply by 5<\/em><\/p>\n\n\n\n

5x<\/em> – 2y<\/em> = 1 multiply by 1<\/em><\/p>\n\n\n\n

Thus you get<\/p>\n\n\n\n

5x<\/em> + 15y<\/em> = 35 <\/p>\n\n\n\n

5x<\/em> – 2y<\/em> = 1.<\/p>\n\n\n\n

5x<\/em> + 15y<\/em> = 35 minus equation 1 with eq. 2; this cancels off both x variables, so we can solve for y<\/em><\/p>\n\n\n\n

5x<\/em> – 2y<\/em> = 1<\/p>\n\n\n\n

17y<\/em> = 34 divide both sides by 17 to isolate y<\/em><\/p>\n\n\n\n

y <\/em>= 2 now, plug the value of y into one of the equations, preferably the original one<\/em><\/p>\n\n\n\n

x<\/em> + 6 = 7 solve for x by isolating it<\/em><\/p>\n\n\n\n

x = 1 write your answer down in the correct format<\/em><\/p>\n\n\n\n

[1, 2] answer<\/em><\/p>\n\n\n\n

<\/p>\n\n\n\n

Practice Questions<\/strong><\/p>\n\n\n\n

  1. <\/li><\/ol>\n\n\n\n

    x<\/em> + y<\/em> = 5<\/p>\n\n\n\n

    2x<\/em> + 3y<\/em> = 13<\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    Answer: [2, 3]<\/p>\n\n\n\n

    <\/p>\n\n\n\n

    2. <\/p>\n\n\n\n

    2x – 2y = -1<\/p>\n\n\n\n

    4x + y = 3<\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    Answer: [1\/2, 1]<\/p>\n\n\n\n

    <\/p>\n\n\n\n

    3 to \u221e. <\/p>\n\n\n\n

    (Look for other sources or ask someone else to create some)<\/p>\n","protected":false},"excerpt":{"rendered":"

    There are a lot of situations where we find ourselves with two-variable equations, but it does seem frustrating trying to solve them. Here’s an example (where the answer is rounded to nearest integer): x + 3y = 7 5x – 2y = 1 There are two methods for solving this equation. Method 1: x + […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[22],"class_list":["post-805","post","type-post","status-publish","format-standard","hentry","category-daily","tag-math"],"_links":{"self":[{"href":"https:\/\/yesrenee.com\/index.php?rest_route=\/wp\/v2\/posts\/805","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/yesrenee.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/yesrenee.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/yesrenee.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/yesrenee.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=805"}],"version-history":[{"count":4,"href":"https:\/\/yesrenee.com\/index.php?rest_route=\/wp\/v2\/posts\/805\/revisions"}],"predecessor-version":[{"id":817,"href":"https:\/\/yesrenee.com\/index.php?rest_route=\/wp\/v2\/posts\/805\/revisions\/817"}],"wp:attachment":[{"href":"https:\/\/yesrenee.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=805"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/yesrenee.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=805"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/yesrenee.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=805"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}