How do you solve the following system: 6x + y = 2, 5x + 8y = -2?

Apr 10, 2016

$\left(x , y\right) = \left(- \frac{22}{43} , \frac{18}{43}\right)$

Explanation:

Solve by elimination substitution

color(blue)(6x+y=2

color(blue)(5x+8y=-2

We can eliminate $8 y$ in the second equation by $y$ in the first equation if we multiply (whole equation) $y$ with $- 8$ to get $- 8 y$

$\rightarrow - 8 \left(6 x + y = 2\right)$

Use distributive property

color(brown)(a(b+c=x)=ab+ac=ax

$\rightarrow - 48 x - 8 y = - 16$

Now,add the above equation to the second equation to eliminate $8 y$

$\rightarrow \left(- 48 x - 8 y = - 16\right) + \left(5 x + 8 y = - 2\right)$

$\rightarrow - 43 x = - 18$

Divide both sides by $- 43$

$\rightarrow \frac{\cancel{- 43} x}{\cancel{- 43}} = \frac{- 18}{-} 43$

color(green)(rArrx=18/43

Because,

color(brown)((-a)/-b=a/b

Now,substitute the value of $x$ to the first equation

$\rightarrow 6 \left(\frac{18}{43}\right) + y = 2$

$\rightarrow \frac{108}{43} + y = 2$

$\rightarrow \frac{108 + 43 y}{43} = 2$

Multiply both sides by $43$

$\rightarrow \frac{108 + 43 y}{\cancel{43}} \cdot \cancel{43} = 2 \cdot 43$

$\rightarrow 108 + 43 y = 86$

Subtract $108$ both sides

$\rightarrow 108 + 43 y - 108 = 86 - 108$

$\rightarrow 43 y = - 22$

Divide both sides by $43$

$\rightarrow \frac{\cancel{43} y}{\cancel{43}} = - \frac{22}{43}$

color(green)(rArry=-22/43

color(blue)(ul bar |(x,y)=(-22/43,18/43)|