Since the trapezoid can be inscribed in a circle, that means angle B + angle D = 180 degree. Since AB is parallel to CD, then angle B + angle C = 180 degree. Therefore, angle D = angle C.

4 0

2 years ago

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−4x+7y+5=0 x−3y=−5 How many solutions does the system have?

xeze [42]

Solution:

Using Substitution Method:

-4x+7y=-5 (Equation 1)

x-3y=-5 (Equation 2)

get the value of x from Equation 2

x=3y-5 (Equation 3)

Put the value of x from Equation 3 in Equation 1

-4(3y-5)+7y=-5

-4(3y)+20+7y=-5

-12y+7y=-5-20

-5y=-25

Negative sign on both sides cancels each other

y=25/5

y=5

Putting value of y in equation 3

x=3(5)-5

x=15-5

x=10

Therefore, [x,y]=[10,5]

Using Elimination Method

-4x+7y=-5 (Equation 1)

x-3y=-5 (Equation 2)

Multiply equation 2 with -4 in order to eliminate the x term

-4(x-3y)=-5*4

-4x+12y=20 (Equation 3)

Adding Equation 1 and 3

-4x+7y=-5

-4x+12y=20

+ - = - (Change Of Sign with x and y terms)

-----------------

0x-5y = -25

-5y=-25

y=5

Substituting y’s value is Equation 1

-4x+7(5)=-5

-4x+35=-5

-4x=-40

Cancellation of negative sign on both sides

x=40/4

x=10

[x,y]=[10,5]

3 0

2 years ago