How do you solve the system by graphing y= 1/4x -1 and y= -2x -10?

$x = - 4$
$y = - 2$

Explanation:

the given system

$y = \frac{1}{4} x - 1$

$y = - 2 x - 10$

Solution

$y = y$

$\frac{1}{4} x - 1 = - 2 x - 10$

Transpose all terms with x on the left side

$\frac{1}{4} x + 2 x = - 10 + 1$

$\left(\frac{1}{4} + 2\right) x = - 9$

$\frac{9}{4} x = - 9$

Multiply now both sides by 4/9

$\frac{4}{9} \cdot \frac{9}{4} x = \frac{4}{9} \left(- 9\right)$

$x = - 4$

to solve for $y$ use equation $y = - 2 x - 10$ and $x = - 4$

$y = - 2 x - 10$

$y = - 2 \left(- 4\right) - 10$

$y = 8 - 10$

$y = - 2$

Checking

With equation $y = \frac{1}{4} x - 1$

$y = \frac{1}{4} x - 1$

$- 2 = \frac{1}{4} \left(- 4\right) - 1$

$- 2 = - 2 \text{ }$correct

~~~~~~~~~~~~~~~~~~~~~~~

Checking

With equation $y = - 2 x - 10$

$y = - 2 x - 10$

$- 2 = - 2 \left(- 4\right) - 10$

$- 2 = - 2 \text{ }$correct

God bless....I hope the explanation is useful

Jun 20, 2016

Solution by graphing below.
$\textcolor{w h i t e}{\text{XXX}} \left(x , y\right) \approx \left(- 4 , - 2\right)$

Explanation:

For each of the given equations select a few (at least two but I would suggest three) values for $x$ and solve for corresponding $y$ values.

{: (color(red)(y=1/4x-1),,," | ",color(blue)(y=-2x-10),,), (,color(red)(underline(x)),color(white)("X")color(red)(underline(y))," | ",,color(white)("X")color(blue)(underline(x)),color(white)("X")color(blue)(underline(y))), (,color(red)(0),color(red)(-1)," | ",,color(white)("X")color(blue)(0),color(blue)(-10)), (,color(red)(4),color(white)("X")color(red)(0)," | ",,color(white)("X")color(blue)(1),color(blue)(-12)), (,color(red)(8),color(white)("X")color(red)(1)," | ",,color(blue)(-1),color(white)("X")color(blue)(-8)) :}

Plot each pair of points which you have calculated and draw a line for each equation's set of points.

The point where the two equation lines intersect provide the coordinates of the system solution.

In this case it appears that $x$ is about $- 4$ and $y$ is about $- 2$.
(This in fact the exact solution but, in general, solving equations by graphing is very dependent on the accuracy of your drawing).