How do you solve the following system?: $4 x + 5 y = 2, y + 5 = 3 x$ $4x + 5y = 2 , y + 5 = 3x$

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How do you solve the following system?: $4 x + 5 y = 2, y + 5 = 3 x$ $4x + 5y = 2 , y + 5 = 3x$

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Answer 1 · 2018-03-05T15:37:13

$x = \frac{27}{19}$ $x = 27/19$ and $y = - \frac{14}{19}$ $y = -14/19$

Explanation:

Let's isolate $y$ $y$ in the second equation

$y = 3 x - 5$ $y = 3x - 5$

Now we can solve for $x$ $x$ in the other equation

$4 x + 5 (3 x - 5) = 2$ $4x + 5 (3x - 5) = 2$

$4 x + 15 x - 25 = 2$ $4x + 15x -25 = 2$

$19 x = 27$ $19x = 27$

$x = \frac{27}{19}$ $x = 27/19$

Now we solve for $y$ $y$

$y = 3 x - 5$ $y = 3x - 5$

$y = 3 (\frac{27}{19}) - 5$ $y = 3 (27/19) - 5$

$y = \frac{81}{19} - \frac{5}{1} \times \frac{19}{19}$ $y = 81/19 - 5/1 xx 19/19$

$y = \frac{81}{19} - \frac{95}{19}$ $y = 81/19 - 95/19$

$y = - \frac{14}{19}$ $y = -14/19$

To check our work, let's substitute $\frac{27}{19}$ $27/19$ for $x$ $x$ and $- \frac{14}{19}$ $-14/19$ for $y$ $y$ in the first equation and solve.

$4 (\frac{27}{19}) + 5 (- \frac{14}{19}) = 2$ $4(27/19) + 5(-14/19) = 2$

$\frac{108}{19} - \frac{70}{19} = \frac{38}{19}$ $108/19 - 70/19 = 38/19$

$\frac{38}{19} = 2 = 2$ $38/19 = 2 = 2$ !

We were right!

Answer 2 · 2018-03-05T15:42:54

$x = \frac{27}{19}, y = - \frac{14}{19}$ $color(blue)(x = 27/19), color(purple)(y = -14 / 19)$

Explanation:

$4 x + 5 y = 2$ $4x + 5y = 2$ Eqn (1)

$y + 5 = 3 x$ $y + 5 = 3x$

$y = 3 x - 5$ $y = 3x - 5$ Eqn (2)

Substituting value of y term in Eqn (1) in terms of x,

$4 x + 5 (3 x - 5) = 2$ $4x + 5(3x - 5) = 2$

$4 x + 15 x - 25 = 2$ $4x + 15x - 25 = 2$

Rearranging variables on L H S, constants on R H S,

$4 x + 15 x = 27$ $4x + 15x = 27$

$19 x = 27$ $19x = 27$ or $x = \frac{27}{19}$ $x = 27/19$

Substituting value of x in Eqn (2),

$y = 3 x - 5 = (3 \cdot (\frac{27}{19})) - 5 = \frac{81 - 95}{19} = - \frac{14}{19}$ $y = 3x - 5 = (3 * (27 / 19)) - 5 = (81 - 95) / 19 = -14/19$

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How do you solve the following system?: $4 x + 5 y = 2, y + 5 = 3 x$ $4x + 5y = 2 , y + 5 = 3x$

2 Answers

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How do you solve the following system?: 4x+5y=2,y+5=3x4x + 5y = 2 , y + 5 = 3x

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How do you solve the following system?: $4 x + 5 y = 2, y + 5 = 3 x$ $4x + 5y = 2 , y + 5 = 3x$