How do you solve the simultaneous equations $4 x + y = 9$ $4x + y = 9$ and $2 x - y = 3$ $2x - y = 3$ ?

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How do you solve the simultaneous equations $4 x + y = 9$ $4x + y = 9$ and $2 x - y = 3$ $2x - y = 3$ ?

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Answer 1 · 2015-07-13T21:14:10

Since both given equations contain similar coefficients for $y$ $y$ , the simplest method is to add the two equations and solving single variable equations to get
$(x, y) = (2, 1)$ $(x,y) =(2,1)$

Explanation:

[1] $XXXX$ $color(white)("XXXX")$ $4 x + y = 9$ $4x+y = 9$
[2] $XXXX$ $color(white)("XXXX")$ $2 x - y = 3$ $2x-y = 3$

Add [1] to [2] giving
[3] $XXXX$ $color(white)("XXXX")$ $6 x = 12$ $6x = 12$
Divide both sides by $6$ $6$
[4] $XXXX$ $color(white)("XXXX")$ $x = 2$ $x = 2$
Using information from [4], replace $x$ $x$ with $2$ $2$ in [1]
[5] $XXXX$ $color(white)("XXXX")$ $4 (2) + y = 9$ $4(2)+y = 9$
Simplify
[6] $XXXX$ $color(white)("XXXX")$ $y = 1$ $y=1$

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How do you solve the simultaneous equations $4 x + y = 9$ $4x + y = 9$ and $2 x - y = 3$ $2x - y = 3$ ?

1 Answer

Explanation:

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How do you solve the simultaneous equations $4 x + y = 9$ $4x + y = 9$ and $2 x - y = 3$ $2x - y = 3$ ?