Question :
Solve the system of equations using the substitution method. Show all works
- y = 5x - 7
- - 3x - 2y = - 12
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Answer :
- [tex] \large \underline{\boxed{\bf{x = 2}}}[/tex]
- [tex] \large \underline{\boxed{\bf{y = 3}}}[/tex]
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Explanation :
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Given :
- y = 5x - 7⠀ ⠀⠀ ⠀ ⠀⠀ - (i)
- - 3x - 2y = - 12⠀ ⠀⠀ ⠀- (ii)
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From equation (i), we have :
[tex] \tt : \implies y = 5x - 7[/tex]
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By Substituting y = 5x - 7 in equation (ii), we get :
[tex] \tt : \implies - 3x - 2(5x - 7) = - 12[/tex]
[tex] \tt : \implies - 3x - 10x + 14 = - 12[/tex]
[tex] \tt : \implies - 13x = - 12 - 14[/tex]
[tex] \tt : \implies - 13x = - 26[/tex]
[tex] \tt : \implies 13x = 26[/tex]
[tex] \tt : \implies x = \dfrac{26}{13}[/tex]
[tex] \tt : \implies x = 2[/tex]
[tex] \large \underline{\boxed{\bf{x = 2}}}[/tex]
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Now, By substituting x = 2 in equation (i), we get :
[tex] \tt : \implies y = 5(2) - 7[/tex]
[tex] \tt : \implies y = 10 - 7[/tex]
[tex] \tt : \implies y = 3[/tex]
[tex] \large \underline{\boxed{\bf{y = 3}}}[/tex]
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Hence, solution of given system of equations are :
- [tex] \large \underline{\boxed{\bf{x = 2}}}[/tex]
- [tex] \large \underline{\boxed{\bf{y = 3}}}[/tex]
