How do I use substitution to find the solution of the system of equations $y=1/3x+7/3$ and $y=-5/4x+11/4$ ?

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How do I use substitution to find the solution of the system of equations $y=1/3x+7/3$ and $y=-5/4x+11/4$ ?

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Answer 1 · 2014-09-26T23:56:27

In this problem we have 2 different expressions that represent the value of $y$ . Because they both represent $y$ we can set them equal to each other.

$(1/3)x+7/3=-(5/4)x+11/4$

Because all of the terms share a common multiple of 12 I will multiply each term by 12 to eliminate the fractions.

$12[(1/3)x+7/3=-(5/4)x+11/4]$

$[(12/3)x+84/3=-(60/4)x+132/4]$

$4x+28=-15x+33$

$19x=5$

$x=5/19$

Substitute in this newly found $x$ -value into one of the original equations.

$y=(1/3)x+7/3$

$y=(1/3)*(5/19)+7/3$

$y=(5/57)+7/3*19/19$

$y=5/57+133/57$

$y=138/57$

$y=46/19$

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How do I use substitution to find the solution of the system of equations $y=1/3x+7/3$ and $y=-5/4x+11/4$ ?

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How do I use substitution to find the solution of the system of equations y=1/3x+7/3y=1/3x+7/3 and y=-5/4x+11/4y=-5/4x+11/4?

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How do I use substitution to find the solution of the system of equations $y=1/3x+7/3$ and $y=-5/4x+11/4$ ?