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Fudgin [204]
3 years ago
7

Find the solution of this system of equations -x-4y=37 -2x-4y=-53

Mathematics
2 answers:
mixer [17]3 years ago
7 0

Answer:

X=90, y =-127/4


Step-by-step explanation:

Subtract the second equation from the first and you get X+ 0y= 90. Replace x=90 in either equation and you get y= -127/4.

Lelu [443]3 years ago
5 0

Answer:

Final answer is x=90, y=-\frac{127}{4}

Step-by-step explanation:

Given equations are:

-x-4y=37 ...(i)

-2x-4y=-53 ...(ii)

multiply (ii) by -1

2x+4y=53 ...(iii)

Add (i) and (iii)

x=90

plug value of x=90 into (i)

-x-4y=37

-90-4y=37

-4y=37+90

-4y=127

y=-\frac{127}{4}

Hence final answer is x=90, y=-\frac{127}{4}


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Step-by-step explanation:

The formula for the equation of a circle is given as:

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Substituting 2 for x and -2 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

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Expanding the bracket

(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²

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a² + b² -4a + 4b + 4 + 4 = r²

a² + b² -4a + 4b + 8 = r²............Equation 1

We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y

Hence,

Substituting 3 for x and 4 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(3 - a)² +(4 - b)² = r²

Expanding the bracket

(3 - a) (3 - a) + (4 - b)(4- b) = r²

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The next step would be to subtract Equation 1 from Equation 2

a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²

a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²

Collecting like terms

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We are going to have to find the values of a and b in other to get our equation of the circle.

Since the center of the circle(a, b) lies on x + y = 2

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