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2 years ago

Solve the simultaneous equation X+3y=13 X-y=5

Mathematics

1 answer:

Andru [333]2 years ago

5 0

Answer:

x = 7

y = 2

Step-by-step explanation:

In the above question, we are given 2 equations which are simultaneous. To solve this equation, we have to find the values of x and y

x + 3y = 13 ........ Equation 1

x - y = 5...........Equation 2

From Equation 2,

x = 5 + y

Substitute 5 + y for x in Equation 1

x + 3y = 13 ........ Equation 1

5 + y + 3y = 13

5 + 4y = 13

4y = 13 - 5

4y = 8

y = 8/4

y = 2

Since y = 2, substitute , 2 for y in Equation 2

x - y = 5...........Equation 2

x - 2 = 5

x = 5 + 2

x = 7

Therefore, x = 7 and y = 2

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One leg of a right triangle is 7 inches longer than the other leg, and the hypotenuse is 35 inches. Find the lengths of the legs

lilavasa [31]

Answer: 21, 28

Step-by-step explanation:

Side #1 = x
Side #2 = x + 7
Hypotenuse = 35

Use the Pythagorean Theorem $a^{2}+b^{2}=c^{2}$ :

a = x
b = x + 7
c = 35

Substitute in the values & solve:

$x^{2}+(x+7)^{2}=35^{2}\\x^{2}+x^{2}+14x+49=1225\\2x^{2}+14x+49-1225=0\\2x^{2}+14x-1176=0\\2(x^{2}+7x-588)=0\\2(x + 28)(x - 21)=0\\x_{1}=-28, x_{2}=21$

-28 is not a possible solution since you can't have negative inches...

a = x = 21
b = x + 7 = 21 + 7 = 28
c = 35

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2 years ago

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Anuta_ua [19.1K]

Answer:

Step-by-step explanation:

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2 years ago

When y=-2, what kind of line does it have horizontal or vertical

Rashid [163]

Answer: Horizontal

Step-by-step explanation: The equation y = -2 can be thought of as y = 0x - 2. So our line has a slope of 0 and a y-intercept of -2.

To graph it, we start with the y-intercept, down 2 units on the y-axis. Now, if the slope of a line is 0, then the line must be flat or horizontal.

So we just draw a horizontal line through the y-intercept of -2.

In fact, when the equation of any line reads y = a number, it's graph will always be a horizontal line. For example, y = 3, y = -10, y = -8 and so on.

Image provided below.