How do solve the following linear system?: $\frac{3}{2} x - 3 y = - \frac{9}{4}, \frac{2}{3} x + 4 y = - 1$ $3/2x - 3y = -9/4 , 2/3x + 4y = -1$ ?

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How do solve the following linear system?: $\frac{3}{2} x - 3 y = - \frac{9}{4}, \frac{2}{3} x + 4 y = - 1$ $3/2x - 3y = -9/4 , 2/3x + 4y = -1$ ?

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Answer 1 · 2016-02-19T11:51:47

$(x, y) = (- \frac{3}{2}, 0)$ $(x,y)=(-3/2,0)$

Explanation:

Given:
[1] $XXX \frac{3}{2} x - 3 y = - \frac{9}{4}$ $color(white)("XXX")3/2x-3y=-9/4$
[2] $XXX \frac{2}{3} x + 4 y = - 1$ $color(white)("XXX")2/3x+4y=-1$
To make the solution easier we will clear the fractions by
multiplying [1] by $4$ $4$ and [2] by $3$ $3$ to get
[3] $XXX 6 x - 12 y = - 9$ $color(white)("XXX")6x-12y=-9$
[4] $XXX 2 x + 12 y = - 3$ $color(white)("XXX")2x+12y=-3$

Adding equations [3] and [4] gives
[5] $XXX 8 x = - 12$ $color(white)("XXX")8x=-12$
and after dividing by $8$ $8$
[6] $XXX x = - \frac{3}{2}$ $color(white)("XXX")x=-3/2$

Substituting $(- \frac{3}{2})$ $(-3/2)$ (from [6]) for $x$ $x$ in [2]
[7] $XXX \frac{2}{3} \times (- \frac{3}{2}) + 4 y = - 1$ $color(white)("XXX")2/3xx(-3/2)+4y=-1$
Simplifying
[8] $XXX y = 0$ $color(white)("XXX")y=0$

Graphically:
graph{(3/2x-3y+9/4)(2/3x+4y+1)=0 [-5.07, 2.725, -1.414, 2.483]}

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How do solve the following linear system?: $\frac{3}{2} x - 3 y = - \frac{9}{4}, \frac{2}{3} x + 4 y = - 1$ $3/2x - 3y = -9/4 , 2/3x + 4y = -1$ ?

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How do solve the following linear system?: $\frac{3}{2} x - 3 y = - \frac{9}{4}, \frac{2}{3} x + 4 y = - 1$ $3/2x - 3y = -9/4 , 2/3x + 4y = -1$ ?