Step-by-step explanation:
As the given equation is
[tex]-x-4y=-10[/tex]
We have to find the ordered pair which satisfies the equation.
So,
[tex]-x-4y=-10[/tex]........[A]
Plug x = 0 in Equation [A] to find the y-intercept
[tex]-(0)-4y=-10[/tex]
[tex]-4y=-10[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-4[/tex]
[tex]\frac{-4y}{-4}=\frac{-10}{-4}[/tex]
[tex]y=\frac{5}{2}[/tex]
So,
when x = 0, then y = 5/2
In other words, (0, 5/2) is the ordered pair of the equation [tex]-x-4y=-10[/tex].
Putting the value of x = 0, and y = 5/2 in Equation [1] for validation of the ordered pair (0, 5/2)
[tex]-x-4y=-10[/tex]
[tex]-0-4(\frac{5}{2} )=-10[/tex]
[tex]-(\frac{20}{2} )=-10[/tex]
[tex]-10=-10[/tex] ∵ L.H.S = R.H.S
Hence, (0, 5/2) is one of the ordered pairs which is a solution to the equation [tex]-x-4y=-10[/tex].
Similarly, x-intercept can be found by putting y = 0 in [tex]-x-4y=-10[/tex].
So,
[tex]-x-4y=-10[/tex]
[tex]-x-4(0)=-10[/tex]
[tex]-x=-10[/tex]
[tex]x=10[/tex]
So, (10, 0) is another ordered pair (x-intercept) which satisfies the equation [tex]-x-4y=-10[/tex].
The graph is also attached for the equation [tex]-x-4y=-10[/tex] where you can easily figure out x and y intercepts.
Keywords: ordered pair, x-intercept, y-intercept, graph, solution
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