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3 years ago

Find the solution of the system of equations 3x+4y=10 and x−y=1. Give the x value followed by the y value, separated by a comma

Mathematics

2 answers:

mote1985 [20]3 years ago

8 0

Answer: the solution is (2, 1)

Step-by-step explanation:

The given system of simultaneous equations is given as

3x+4y=10 - - - - - - - - - - - - -1

x−y=1 - - - - - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 1 an equation 2 by 3. It becomes

3x + 4y = 10

3x - 3y = 3

Subtracting, it becomes

7y = 7

Dividing the left hand side and the right hand side of the equation by 7, it becomes

7y/7 = 7/7

y = 1

Substituting y = 1 into equation 2, it becomes

x - 1 = 1

Adding 1 to the left hand side and the right hand side of the equation, it becomes

x - 1 + 1= 1 + 1

x = 2

GREYUIT [131]3 years ago

4 0

Answer:

Solution of the system is (2,1).

Step-by-step explanation:

We are given the following system of equation:

$3x+4y=10\\x - y = 1$

We would use the elimination method to solve the following system of equation.

Multiplying the second equation by 4 and adding the two equation we gwt:

$3x + 4y = 10\\4\times (x-y = 1)\\\Rightarrow 4x - 4y = 4\\\text{Adding equations}\\3x + 4y + (4x-4y) = 10 + 4\\7x = 14\\\Rightarrow x = 2\\\text{Substituting value of x in second equation}\\2 - y = 1\\\Rightarrow y = 1$

Solution of the system is (2,1).

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Please help with this question asap

stepladder [879]

Pythagoras theorem: leg 1 squared + leg 2 squared = hypotenuse squared

In the diagram, the triangle has angles 90 and 45. So the other angle in the triangle must be 45 degrees as well. (180 - 90 -45 = 45)

This means it is an isosceles triangle (since two angles are the same), so the two legs have the same length.

So we can say that length of leg1 = x, and the length of leg2 also equals x

Now let's use pythagoras' theorem:

leg1 = x

leg2 = x

hypotenuse = 16

x^2 + x^2 = 16^2

2x^2 = 16^2

2x^2 = 256

x^2 = 128

x = √(128)

x = 8√2

3 0

3 years ago

Find the length of the longest side of the rectangle whose vertices are given. a(2, 1), b(5, 4), c(0, 3), d(3, 6)

aleksandr82 [10.1K]

First, you plot the coordinates to visualize the problem clearly. As you can see in the picture, the longest sides could either be one of those marked in red. This could be initially determined when you use visual estimation. We measure this using the distance formula: d = √[(x2-x1)^2 + (y2-y1)^2)]

Between coordinates (0,3) and (3,6)
d = √[(3-0)^2 + (6-3)^2)]
d= 4.24 units

Between coordinates (2,1) and (5,4)
d = √[(5-2)^2 + (4-1)^2)]
d= 4.24 units

They are of equal length. Both are the longest sides which measures 4.24 units.