Find three solutions of linear equation 7x \u2013 5y = 35 in two variables.<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Correct Answer:<\/strong><\/p>\n\n\n\n The linear equation is:<\/p>\n\n\n\n 7x\u22125y=357x – 5y = 35<\/p>\n\n\n\n We want to find three pairs (x,y)(x, y) that satisfy this equation.<\/p>\n\n\n\n 7x\u22125y=357x – 5y = 35<\/p>\n\n\n\n Rearranging for yy: \u22125y=35\u22127x\u2005\u200a\u27f9\u2005\u200ay=7x\u2212355-5y = 35 – 7x \\implies y = \\frac{7x – 35}{5}<\/p>\n\n\n\n Let’s pick some convenient values for xx:<\/p>\n\n\n\n y=7(0)\u2212355=\u2212355=\u22127y = \\frac{7(0) – 35}{5} = \\frac{-35}{5} = -7<\/p>\n\n\n\n Solution: (0,\u22127)(0, -7)<\/p>\n\n\n\n y=7(5)\u2212355=35\u2212355=0y = \\frac{7(5) – 35}{5} = \\frac{35 – 35}{5} = 0<\/p>\n\n\n\n Solution: (5,0)(5, 0)<\/p>\n\n\n\n y=7(10)\u2212355=70\u2212355=355=7y = \\frac{7(10) – 35}{5} = \\frac{70 – 35}{5} = \\frac{35}{5} = 7<\/p>\n\n\n\n Solution: (10,7)(10, 7)<\/p>\n\n\n\n The equation 7x\u22125y=357x – 5y = 35 is a linear equation in two variables, meaning its graph on the Cartesian plane is a straight line. Any point (x,y)(x, y) on this line satisfies the equation. To find solutions, we typically pick a value for one variable and solve for the other.<\/p>\n\n\n\n In this case, it is easier to solve for yy in terms of xx: y=7x\u2212355y = \\frac{7x – 35}{5}<\/p>\n\n\n\n This expression tells us exactly what yy must be for any chosen xx so that the equation holds true.<\/p>\n\n\n\n Choosing x=0x=0, we get y=\u22127y=-7. This point (0,\u22127)(0, -7) lies on the line and is one solution. Similarly, when x=5x=5, y=0y=0, giving another solution (5,0)(5,0). When x=10x=10, y=7y=7 yields the solution (10,7)(10,7).<\/p>\n\n\n\n These three solutions show how different values of xx correspond to specific values of yy, and all satisfy the original equation. The set of all such points (x,y)(x, y) forms the entire line defined by the equation.<\/p>\n\n\n\n Since this is a linear equation, infinitely many solutions exist, but listing a few helps to understand the relationship between xx and yy. This process is common for linear equations in two variables and is essential for graphing and analyzing linear relationships.<\/p>\n\n\n\n If you graph these points on a coordinate plane and connect them, you’ll see a straight line representing all solutions to the equation 7x\u22125y=357x – 5y = 35.<\/p>\n","protected":false},"excerpt":{"rendered":" Find three solutions of linear equation 7x \u2013 5y = 35 in two variables. The correct answer and explanation is: Correct Answer: The linear equation is: 7x\u22125y=357x – 5y = 35 We want to find three pairs (x,y)(x, y) that satisfy this equation. Step 1: Express yy in terms of xx 7x\u22125y=357x – 5y = […]<\/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-20640","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20640","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=20640"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20640\/revisions"}],"predecessor-version":[{"id":20642,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/20640\/revisions\/20642"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=20640"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=20640"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=20640"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Express yy in terms of xx<\/h3>\n\n\n\n
\n\n\n\nStep 2: Choose values for xx and find corresponding yy<\/h3>\n\n\n\n
\n
\n
\n
\n\n\n\nSummary of Solutions:<\/h3>\n\n\n\n
\n
\n\n\n\nExplanation (300 words):<\/h3>\n\n\n\n