{"id":110,"date":"2022-04-13T10:01:22","date_gmt":"2022-04-13T10:01:22","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=110"},"modified":"2024-12-20T07:12:52","modified_gmt":"2024-12-20T07:12:52","slug":"e-6-solve-a-pair-of-equations-using-substitution","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/e-6-solve-a-pair-of-equations-using-substitution\/","title":{"rendered":"E.6 Solve a pair of equations using substitution"},"content":{"rendered":"\n

Solve a pair of equations using substitution<\/strong><\/h2>\n\n\n\n

key notes:<\/p>\n\n\n\n

To solve using substitution, follow these four steps:<\/p>\n\n\n\n

Step 1: Isolate a variable.<\/p>\n\n\n\n

Step 2: Plug the result of Step 1 into the other equation and solve for one variable.<\/p>\n\n\n\n

Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable.<\/p>\n\n\n\n

Step 4: State the solution.<\/p>\n\n\n\n

The substitution method is easiest to use in one of these situations.<\/p>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
\n
\n

Solve using substitution. <\/p>\n\n\n\n

x = -9<\/p>\n\n\n\n

-4x – 9y = -9<\/p>\n\n\n\n

( _____ , _____ )<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n

Use substitution to solve the simultaneous equations:<\/p>\n\n\n\n

x = \u20139
\u20134x \u2212 9y = \u20139<\/p>\n\n\n\n

Step 1: Isolate a variable.<\/p>\n\n\n\n

The variable x is already isolated in the first equation.<\/p>\n\n\n\n

Step 2: Plug the result of Step 1 into the other equation and solve for one variable.<\/p>\n\n\n\n

Plug x = \u20139 into the other equation, \u20134x \u2212 9y = \u20139, and find the value of y.<\/p>\n\n\n\n

\u20134x \u2212 9y = \u20139<\/p>\n\n\n\n

\u20134(\u20139) \u2212 9y = \u20139 Plug in x = \u20139<\/p>\n\n\n\n

36 \u2212 9y = \u20139 Multiply<\/p>\n\n\n\n

\u20139y = \u201345 Subtract 36 from both sides<\/p>\n\n\n\n

y = 5 Divide both sides by \u20139<\/p>\n\n\n\n

Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable.<\/p>\n\n\n\n

The first equation already shows that x = \u20139, so it is not necessary to plug in and solve for x.<\/p>\n\n\n\n

Step 4: State the solution.<\/p>\n\n\n\n

Since x = \u20139 and y = 5, the solution is (\u20139, 5).<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

Solve using substitution. <\/p>\n\n\n\n

y = 1<\/p>\n\n\n\n

x – 7y = -3<\/p>\n\n\n\n

( _____ , _____ )<\/p>\n<\/div><\/div>\n\n\n\n

Use substitution to solve the simultaneous equations:<\/p>\n\n\n\n

y = 1
x \u2212 7y = \u20133<\/p>\n\n\n\n

Step 1: Isolate a variable.<\/p>\n\n\n\n

The variable y is already isolated in the first equation.<\/p>\n\n\n\n

Step 2: Plug the result of Step 1 into the other equation and solve for one variable.<\/p>\n\n\n\n

Plug y = 1 into the other equation, x \u2212 7y = \u20133, and find the value of x.<\/p>\n\n\n\n

x \u2212 7y = \u20133<\/p>\n\n\n\n

x \u2212 7(1) = \u20133 Plug in y = 1<\/p>\n\n\n\n

x \u2212 7 = \u20133 Multiply<\/p>\n\n\n\n

x = 4 Add 7 to both sides<\/p>\n\n\n\n

Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable.<\/p>\n\n\n\n

The first equation already shows that y = 1, so it is not necessary to plug in and solve for y.<\/p>\n\n\n\n

Step 4: State the solution.<\/p>\n\n\n\n

Since x = 4 and y = 1, the solution is (4, 1).<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

Solve using substitution. <\/p>\n\n\n\n

x = 10<\/p>\n\n\n\n

-10x – 10y = -10<\/p>\n\n\n\n

( ___ , ____ ) <\/p>\n<\/div><\/div>\n\n\n\n

Use substitution to solve the simultaneous equations:<\/p>\n\n\n\n

x = 10
\u201310x \u2212 10y = \u201310<\/p>\n\n\n\n

Step 1: Isolate a variable.<\/p>\n\n\n\n

The variable x is already isolated in the first equation.<\/p>\n\n\n\n

Step 2: Plug the result of Step 1 into the other equation and solve for one variable.<\/p>\n\n\n\n

Plug x = 10 into the other equation, \u201310x \u2212 10y = \u201310, and find the value of y.<\/p>\n\n\n\n

\u201310x \u2212 10y = \u201310<\/p>\n\n\n\n

\u201310(10) \u2212 10y = \u201310 Plug in x = 10<\/p>\n\n\n\n

\u2013100 \u2212 10y = \u201310 Multiply<\/p>\n\n\n\n

\u201310y = 90 Add 100 to both sides<\/p>\n\n\n\n

y = \u20139 Divide both sides by \u201310<\/p>\n\n\n\n

Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable.<\/p>\n\n\n\n

The first equation already shows that x = 10, so it is not necessary to plug in and solve for x.<\/p>\n\n\n\n

Step 4: State the solution.<\/p>\n\n\n\n

Since x = 10 and y = \u20139, the solution is (10, \u20139).<\/p>\n<\/div><\/div>\n\n\n\n

lets practice:<\/p>\n\n\n\n

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Solve a pair of equations using substitution key notes: To solve using substitution, follow these four steps: Step 1: Isolate a variable. Step 2: Plug the result of Step 1 into the other equation and solve for one variable. Step 3: Plug the result of Step 2 into one of the original equations and solveContinue reading “E.6 Solve a pair of equations using substitution”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-110","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/110","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=110"}],"version-history":[{"count":26,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/110\/revisions"}],"predecessor-version":[{"id":15442,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/110\/revisions\/15442"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}