Answer:
There is NO Solution to the given system of equations
Step-by-step explanation:
We notice that the two equations in the system are given in sloe-intercept form:
[tex]\left \{ {{y=\frac{1}{2} x+1} \atop {y=\frac{1}{2} x-4}} \right.[/tex]
and they are showing to both have slope equal to [tex]\frac{1}{2}[/tex]. On the other hand, their y-intercepts don't coincide (one is "+1", while the other one is "-4") so we are in the presence of two parallel lines that do not overlap. Therefore, they shouldn't have any point of intersection that would give the a common y-value for the same x-value.
To confirm this, we can try to solve the system, in particular using substitution, since both equations are showing how their "y" values can be written in terms of 'x". we can then replace the expression for the y-value of the first one to replace the "y-value" of the second one as shown below:
[tex]eq\,1)\,\,\,y=\frac{1}{2} x+1\\eq\,2)\,\,\,y=\frac{1}{2} x-4\\\,\,\\\frac{1}{2} x+1=\frac{1}{2} x-4[/tex]
And now try to solve for "x" by grouping all terms in "x" on one side of the equal sign, and all pure numerical values on the other side:
[tex]\frac{1}{2} x-\frac{1}{2} x=-1-4\\0=-5[/tex]
So we find ourselves with all the variables gone,and with a statement which is mathematically incorrect "0=-5", what is called in math an "absurd".
This tells us that it is impossible to find a solution to the equation. There is no (x y) pair that could satisfy it.
