Answer
b.) The system is consistent according to the graph.
c.) The solution is approximately $x = \frac{1}{2}, y = -\frac{1}{4}$.
d.) By adding -1/4 times Equation 1 to Equation 2, we can then solve that $y = -\frac{1}{4}$. Through back substitution, we can solve that $x = \frac{1}{2}$.
e.) Both solutions are identical, we can conclude that the system is consistent and the solution is $x = \frac{1}{2}, y = -\frac{1}{4}$.
Work Step by Step
b.) By graphing the equations, we can see that they intersect and are therefore consistent.
d.) By adding $-\frac{1}{4}$ times Equation 1 to Equation 2, we can then eliminate the $x$ variable in Equation 2.
$2x -8y = 3$
$0x + 3y = -\frac{3}{4}$
We can then conclude from the modified Equation 2, that $y = -\frac{1}{4}$. This value can then be substituted into Equation 1 to then solve for $x$.
$2x-8*(-\frac{1}{4}) = 3$
$2x = 1$
$x = \frac{1}{2}$
