Question

How do you solve the system by graphing $2x-y=4$ and $4x-2y=-8?$

Answer 1

As we know that the above equation has to be solved graphically we can be plotted on a coordinate plane.So we have to find the slope and interception on the planes.

Complete step by step solution: As we want to solve the above equation in graphing form i.e. $2x-y=-8$
So,
Now we want to convert $2x-y=4$
Thus slope intercept we get
$y=2x-4$
i.e. $2$ is the given slope and now intercepting it an $y-$axis.
i.e. $-4.$
So now further solving the equation $4x-2y=-8$ into slope, we get
$2y=4x+8$ or $y=2x+4$
So, the slope is $2$
And now on $y-$axis is $4$
Thus we are seeing the above equation we get, that the line are parallel.
Hence, we will get no solution.
Graph \left\\{ \left( 2x-y-4 \right)\left( 4x-2y+8 \right)=0\left[ -10,10,-5,5 \right] \right\\}

Additional Information:
We can also solve such questions by other ways,
Like here, we can use either substitution method or any alternate method.
As, we have,
$2x - y = 4$ and $4x - 2y = - 8$
Here, the value of the coefficient of x In first equation is 2 and the value of the coefficient of x in the second equation is 4.
So, for solving the question,
We can make the value of coefficient of x in both the equations,
For that,
We need to multiply the first equation by 4 and the second equation by 2.
Then after subtracting the formed equations we can determine the value of x and y.
As we had solved the equation above, we can further solve it.
Example: $2x=4$ and $y=-3$
Now we are taking lines passing through $x=\dfrac{4}{2}=2$
Further the next equation i.e. horizontal line. $y=-3$
Above two point intersect at $P$ i.e. $\left( 2,-3 \right)$

Note:
We can also have example
$x-2y=-2$ and $x-2y=3$
Now taking the first equation
$x-2y=-2$
Now establishing the equation of $x$ and $y$with zero $\left( 0,1 \right)$ and $\left( -2,0 \right)$
Now further solving the second equation
$x-2y=3$
$\left( 0,-1\dfrac{1}{2} \right)$ and $\left( 3,0 \right)$