How do you solve the following system: $10 y = 42 + 2 x, y = \frac{3}{4} x + 3$ $10y=42+2x , y= 3/4x+3$ ?

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Answer 1 · 2016-04-06T06:46:35

$x = \frac{24}{11}$ $x=24/11$
$y = \frac{51}{11}$ $y=51/11$

$10 y = 42 + 2 x (1)$ $10y=42+2x" (1)"$

$expand the second equation by 10$ $"expand the second equation by 10"$

$y = \frac{3}{4} x + 3 (2)$ $y=3/4x+3" (2)"$

$10 \cdot y = 10 \cdot (\frac{3}{4} x + 3)$ $color(red)10*y=color(red)10*(3/4x+3)$

$10 y = \frac{30}{4} x + 30 (3)$ $10y=30/4x+30" (3)"$

$so left side of the equations (1) and (3)are equal$ $"so left side of the equations (1) and (3)are equal"$

$we can write:$ $"we can write:"$

$42 + 2 x = \frac{30}{4} x + 30$ $42+2x=30/4x+30$

$2 x - 30 \frac{x}{4} = 30 - 42$ $2x-30x/4=30-42$

$\frac{8 x - 30 x}{4} = - 12$ $(8x-30x)/4=-12$
$- 22 x = - 4 \cdot 12$ $-22x=-4*12$

$22 x = 48 x = \frac{48}{22}$ $22x=48" "x=48/22$
$x = \frac{24}{11}$ $x=24/11$

$now use the equation (1)$ $" now use the equation (1)"$

$10 y = 42 + 2 (\frac{24}{11})$ $10y=42+2(24/11)$

$10 y = 42 + \frac{48}{11}$ $10y=42+48/11$

$10 y = \frac{462 + 48}{11}$ $10y=(462+48)/11$

$y=(51cancel(0))/(11cancel(0))$

$y=51/11$

How do you solve the following system: 10y=42+2x , y= 3/4x+3 10y=42+2x,y=34x+310y=42+2x , y= 3/4x+3 ?