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How do you solve the system of equations: y = -3x + 5 and 5x - 4y = -3?

1 Answer

Aug 7, 2015

$(x, y) = (1, 2)$ $(x,y) = (1,2)$

Explanation:

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

Since [1] gives us an expression for $y$ $y$ in terms of $x$ $x$
the obvious solution method would be to substitute this expression for $y$ $y$ in [2]
[3] $XXXX$ $color(white)("XXXX")$ 5x-4(-3x+5)=-3#

Simplifying the left side
[4] $XXXX$ $color(white)("XXXX")$ $17 x - 20 = - 3$ $17x-20 = -3$

Adding 20 to both sides:
[5] $XXXX$ $color(white)("XXXX")$ $17 x = 17$ $17x = 17$

Dividing by 17
[6] $XXXX$ $color(white)("XXXX")$ $x = 1$ $x=1$

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

Simplifying
[8] $XXXX$ $color(white)("XXXX")$ $y = 2$ $y=2$

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