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How do you solve $- 6 x + 10 y = 5$ $-6x + 10y = 5$ and $- 2 x + 3 y = - 1$ $-2x + 3y = -1$ ?

1 Answer

Jul 24, 2015

$(x, y) = (\frac{25}{2}, 8)$ $(x,y) = (25/2, 8)$

Explanation:

[1] $XXXX$ $color(white)("XXXX")$ $- 6 x + 10 y = 5$ $−6x+10y=5$
[2] $XXXX$ $color(white)("XXXX")$ $- 2 x + 3 y = - 1$ $−2x+3y=−1$

Multiply [2] by 3
[3] $XXXX$ $color(white)("XXXX")$ $- 6 x + 9 x = - 3$ $-6x+9x = -3$

Subtract [3] from [1]
[4] $XXXX$ $color(white)("XXXX")$ $y = 8$ $y = 8$

Substitute $8$ $8$ for $y$ $y$ in [2]
[5] $XXXX$ $color(white)("XXXX")$ $- 2 x + 3 (8) = - 1$ $-2x+3(8) = -1$

[6] $XXXX$ $color(white)("XXXX")$ $2 x = 25$ $2x = 25$

Divide by $2$ $2$
[7] $XXXX$ $color(white)("XXXX")$ $x = \frac{25}{2}$ $x = 25/2$

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