{"id":37360,"date":"2025-06-25T17:52:22","date_gmt":"2025-06-25T17:52:22","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=37360"},"modified":"2025-06-25T17:58:17","modified_gmt":"2025-06-25T17:58:17","slug":"solve-the-system-of-equations","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/solve-the-system-of-equations\/","title":{"rendered":"Solve the system of equations 2x + 7y =3 x = -4y x = y"},"content":{"rendered":"\n

Solve the system of equations 2x + 7y =3 x = -4y x = y<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

We are given a system of three equations:<\/p>\n\n\n\n

    \n
  1. 2x+7y=32x + 7y = 32x+7y=3<\/li>\n\n\n\n
  2. x=\u22124yx = -4yx=\u22124y<\/li>\n\n\n\n
  3. x=yx = yx=y<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Step 1: Use substitution from equations (2) and (3)<\/h3>\n\n\n\n

    From equation (2):
    x=\u22124yx = -4yx=\u22124y
    From equation (3):
    x=yx = yx=y<\/p>\n\n\n\n

    Since both expressions are equal to xxx, we can set them equal to each other:\u22124y=y-4y = y\u22124y=y<\/p>\n\n\n\n

    Step 2: Solve for yyy<\/h3>\n\n\n\n

    \u22124y=y\u22124y\u2212y=0\u22125y=0y=0-4y = y \\\\ -4y – y = 0 \\\\ -5y = 0 \\\\ y = 0\u22124y=y\u22124y\u2212y=0\u22125y=0y=0<\/p>\n\n\n\n

    Step 3: Substitute y=0y = 0y=0 back to find xxx<\/h3>\n\n\n\n

    Using equation (3), x=yx = yx=y:x=0x = 0x=0<\/p>\n\n\n\n

    \n\n\n\n

    Step 4: Check the solution in all three equations<\/h3>\n\n\n\n
      \n
    • Equation (1): 2x+7y=32x + 7y = 32x+7y=3
      Substitute x=0x = 0x=0, y=0y = 0y=0: 2(0)+7(0)=0\u226032(0) + 7(0) = 0 \\neq 32(0)+7(0)=0\ue020=3<\/li>\n<\/ul>\n\n\n\n

      This result shows that the pair (0,0)(0, 0)(0,0) does not<\/strong> satisfy the first equation. Therefore, there is no solution<\/strong> that satisfies all three equations at once.<\/p>\n\n\n\n

      \n\n\n\n

      Final Answer:<\/h3>\n\n\n\n

      There is no solution<\/strong> to this system of equations. The three equations are inconsistent<\/strong> when considered together.<\/p>\n\n\n\n

      \n\n\n\n

      Explanation <\/h3>\n\n\n\n

      To solve a system of equations, the goal is to find a set of values for the variables that make all equations true at the same time. In this case, the system includes three equations involving two variables: xxx and yyy.<\/p>\n\n\n\n

      We start with two simpler equations: x=\u22124yx = -4yx=\u22124y and x=yx = yx=y. By setting these two expressions equal to each other, we find a potential relationship between xxx and yyy. Setting \u22124y=y-4y = y\u22124y=y and solving gives y=0y = 0y=0. Substituting this value into either equation gives x=0x = 0x=0.<\/p>\n\n\n\n

      So, the point (0,0)(0, 0)(0,0) satisfies the second and third equations. However, to be a valid solution to the system, this point must also satisfy the first equation: 2x+7y=32x + 7y = 32x+7y=3. Substituting x=0x = 0x=0 and y=0y = 0y=0 into the first equation gives 0+0=00 + 0 = 00+0=0, which does not equal 3. This means the point (0,0)(0, 0)(0,0) fails the first equation.<\/p>\n\n\n\n

      Because the only possible point that works with the second and third equations does not satisfy the first equation, there is no point that satisfies all three equations at the same time. Therefore, the system is inconsistent, and we conclude that there is no solution.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Solve the system of equations 2x + 7y =3 x = -4y x = y The Correct Answer and Explanation is: We are given a system of three equations: Step 1: Use substitution from equations (2) and (3) From equation (2):x=\u22124yx = -4yx=\u22124yFrom equation (3):x=yx = yx=y Since both expressions are equal to xxx, we […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37360","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37360","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=37360"}],"version-history":[{"count":3,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37360\/revisions"}],"predecessor-version":[{"id":37547,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37360\/revisions\/37547"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37360"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37360"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37360"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}