# Thread: [SOLVED] More Sim Equations

1. ## [SOLVED] More Sim Equations

$\displaystyle X + 7Y = 6$
$\displaystyle 3X + 5Y = 14$

I still cant get my head around this!

2. For example multiply the first equation (both sides) by 3: $\displaystyle 3X + 21Y = 18$ and subtract from this the other equation: $\displaystyle (3-3)X+(21-5)Y=18-14 \Leftrightarrow 16Y=4\Leftrightarrow Y=\frac {4}{16}=\boxed{\frac 14=0.25}$ which you can substitute in one of the original equation: $\displaystyle X+7\cdot\frac 14=6\Leftrightarrow X=6-\frac 74=\boxed{\frac {17}4=4.25}$.

$\displaystyle X + 7Y = 6$
$\displaystyle 3X + 5Y = 14$

I still cant get my head around this!

$\displaystyle 3x+21y=18$ -------------1

$\displaystyle 3x+5y=14$ --------------2

2-1

Therefore , 16y=4 , y=1/4 , then continue to solve for x .

4. $\displaystyle x = \frac{17}{4}, y = \frac{1}{4}$

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$\displaystyle x = \frac{17}{4}, y = \frac{1}{4}$

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Yeah.

$\displaystyle X + 7Y = 6$
$\displaystyle 3X + 5Y = 14$

I still cant get my head around this!

try this, substitution method

$\displaystyle X + 7Y = 6$

$\displaystyle 3X + 5Y = 14$

$\displaystyle x=6-7y$

$\displaystyle 3(6-7y)+5y=14$

$\displaystyle 18-21y+5y=14$

$\displaystyle 18-14=21y-5y$

$\displaystyle 4=16y$

$\displaystyle y=\frac{1}{4}$

then substitute

$\displaystyle x+7y=6$

$\displaystyle x+\frac{7}{4}=6$

$\displaystyle x=6-\frac{7}{4}$

$\displaystyle x=\frac{24-7}{4}$

$\displaystyle x=\frac{17}{4}$

check

$\displaystyle \frac{17}{4}+7{1}{4}=6$

$\displaystyle \frac{24}{4}=6$

$\displaystyle 6=6$

$\displaystyle 3x+5y=14$

$\displaystyle 3*\frac{17}{4}+5*\frac{1}{4}=14$

$\displaystyle \frac{51+5}{4}=14$

$\displaystyle \frac{56}{4}=14$

$\displaystyle 56=56$