How do you solve the following system?: $y = 2 x - 3, 5 x + 3 y = - 3$ $y=2x-3 , 5x + 3y = -3$

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Answer 1 · 2016-03-14T08:41:32

$x, y = \frac{6}{11}, - \frac{21}{11}$ $x,y=6/11,-21/11$

$y = 2 x - 3$ $color(blue)(y=2x-3$

$5 x + 3 y = - 3$ $color(blue)(5x+3y=-3$

Substitute the value of $y$ $y$ to the second equation

$\to 5 x + 3 (2 x - 3) = - 3$ $rarr5x+3(2x-3)=-3$

Use distributive property $a (b + c) = a b + a c$ $color(brown)(a(b+c)=ab+ac$

$\to 5 x + 6 x - 9 = - 3$ $rarr5x+6x-9=-3$

$\to 11 x - 9 = - 3$ $rarr11x-9=-3$

$\to 11 x = - 3 + 9$ $rarr11x=-3+9$

$\to 11 x = 6$ $rarr11x=6$

#color(green)(rArrx=6/1

Substitute the value of $x$ $x$ to the first equation

$\to y = 2 (\frac{6}{11}) - 3$ $rarry=2(6/11)-3$

$\to y = \frac{12}{11} - 3$ $rarry=12/11-3$

$\Rightarrow y = - \frac{21}{11}$ $color(green)(rArry=-21/11$

How do you solve the following system?: y=2x−3,5x+3y=−3y=2x-3 , 5x + 3y = -3