Given the system of equations below,explain if (6,-9) is a solution or not.
1 answer:
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9514 1404 393
Answer:
x +4y = -5
Step-by-step explanation:
The equation of the perpendicular line can be found by swapping the x- and y-coefficients and negating one of them. The new constant can be found by substituting the point values into the equation.
3x +12y = 3(-5) +12(0)
3x +12y = -15
We notice that all of the values include a factor of 3. We can divide that out to put the equation in standard form:
x + 4y = -5
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.