What is the equation of the directrix of the parabola given by the equation (y − 3)2 = 8(x − 5)?
1 answer:
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The two linear equations in two variable is:
12 x + 3 y = 40
7 x - 4 y = 38
(a) For a system of equations in two Variable
a x + by = c
p x + q y = r
It will have unique solution , when
As, you can see that in the two equation Provided above
So, we can say the system of equation given here has unique solution.
(b). If point (2.5, -3.4) satisfies both the equations, then it will be solution of the system of equation, otherwise not.
1. 12 x+3 y=40
2. 7 x-4 y=38
Substituting , x= 2.5 , and y= -3.4 in equation (1) and (2),
L.H.S of Equation (1)= 1 2 × 2.5 + 3 × (-3.4)
= 30 -10.20
= 19.80≠ R.H.S that is 40.
Similarly, L H S of equation (2)= 7 × (2.5) - 4 × (-3.4)
= 17.5 +13.6
= 31.1≠R HS that is 38
So, you can Write with 100 % confidence that point (2.5, -3.4) is not a solution of this system of the equation.
Answer:
<h2>If we placed the number 10 in the box, we obtain a system of equations with infinitely many solutions.</h2>Step-by-step explanation:
The given system is
<em>It's important to know that a system with infinitely many solutions, it's a system that has the same equation</em>, that is, both equation represent the same line, or as some textbooks say, one line is on the other one, so they have inifinitely common solutions.
Having said that, the first thing we should do here is reorder the system
This way, you can compare better both equations. If you look closer, observe that the second equation is double, that is, it can be obtained by multiplying a factor of 2 to the first one, that is
So, by multiplying such factor, we obtaine the second equation. Observe that must be equal to 10, that way the system would have infinitely solutions.
Therefore, the answer is 10.