How do you solve the following linear system: $3x + y = -6 , 3x + 2y = 9$ ?

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Answer 1 · 2015-11-13T04:13:49

$color(green)(x = -7$
$color(green)( y = 15$

$3x + y = -6$ --------(1)
$3x + 2y = 9$ ------(2)

To solve the equation, we need to find the value of $x and y$

The fastest way to solve for the value of $y$ would be by subtracting equation (1) from equation (2)

$(3x + 2y) - (3x+y) = 9 - (-6)$

$cancel(3x) - cancel(3x) + 2y - y = 9 + 6$

$color(green)( y = 15$

To get the value of $x$ , we can substitute this value of $y$ in any of the two equations

Substituting $y = 15$ in the first equation, we get

$3x + 15 = -6$

Transposing 15 to the right side gives us

$3x = -6-15$

$3x = -21$

$x = -21/3$

$color(green)(x = -7$

How do you solve the following linear system: 3x + y = -6 , 3x + 2y = 9 3x + y = -6 , 3x + 2y = 9 ?