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How do you solve the system of equations: -3x+y=-4 and 2x-y=1?

1 Answer

Aug 12, 2015

Add the given equations together to get an equation in terms or just $x$ $x$ ; solve for $x$ $x$ ; then use the solution value in one of the given equations to determine $y$ $y$
$(x, y) = (- 5, - 11)$ $(x,y) = (-5, -11)$

Explanation:

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

Adding [1] and [2]
[3] $XXXX$ $color(white)("XXXX")$ $- x = 5$ $-x = 5$
Multiplying by $(- 1)$ $(-1)$
[4] $XXXX$ $color(white)("XXXX")$ $x = - 5$ $x = -5$

Substituting $(- 5)$ $(-5)$ for $x$ $x$ in [1]
[5] $XXXX$ $color(white)("XXXX")$ $- 3 (- 5) + y = 4$ $-3(-5) + y = 4$

Simplifying
[6] $XXXX$ $color(white)("XXXX")$ $y = - 11$ $y = -11$

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