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How do you solve the simultaneous equations $3 x + 4 y = 7$ $3x + 4y = 7$ and $5 x - 2 y = 16$ $5x - 2y = 16$ ?

1 Answer

Jul 22, 2015

$(x, y) = (3, - \frac{1}{2})$ $(x, y) = (3, -1/2)$

Explanation:

[1] $XXXX$ $color(white)("XXXX")$ $3 x + 4 y = 7$ $3x+4y = 7$
[2] $XXXX$ $color(white)("XXXX")$ $5 x - 2 y = 16$ $5x-2y = 16$

Multiply [2} by 2 giving
[3] $XXXX$ $color(white)("XXXX")$ $10 x - 4 y = 32$ $10x-4y = 32$

Add [1] and [3]
[4] $XXXX$ $color(white)("XXXX")$ $13 x = 39$ $13x = 39$

Divide both sides by 13
[5] $XXXX$ $color(white)("XXXX")$ $x = 3$ $x = 3$

Substitute $3$ $3$ for $x$ $x$ in [1]
[6] $XXXX$ $color(white)("XXXX")$ $3 (3) + 4 y = 7$ $3(3) +4y = 7$

Simplify
[7] $XXXX$ $color(white)("XXXX")$ $4 y = - 2$ $4y = -2$

[8] $XXXX$ $color(white)("XXXX")$ $y = - \frac{1}{2}$ $y = -1/2$

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