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In parallelogram DEFG, DH = x + 1, HF = 3y,
GH=3x−4,and HE = 5y + 1. Find the values of x and y. The diagram is not drawn to scale

In parallelogram DEFG DH x 1 HF 3y GH3x4and HE 5y 1 Find the values of x and y The diagram is not drawn to scale class=

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ANSWER

[tex]x = 5 \: and \: = 2[/tex]

EXPLANATION


The diagonals of a parallelogram bisects each other.

Therefore

[tex]DH=HF[/tex]


This implies that,

[tex]x + 1 = 3y[/tex]

We make x the subject to get,

[tex]x = 3y - 1...eqn1[/tex]

Similarly,


[tex]GH=HE[/tex]

[tex]3x - 4 = 5y + 1[/tex]


This implies that,

[tex]3x - 5y = 5...eqn2[/tex]


We substitute equation (1) in to equation (2) to get,

[tex]3(3y - 1) - 5y = 5[/tex]


We expand the bracket to get,

[tex]9y - 3 - 5y = 5[/tex]


We group like terms to get,


[tex]9y - 5y = 5 + 3[/tex]


[tex]4y = 8[/tex]

Divide both sides by 4 to obtain,

[tex]y = 2[/tex]


We put the value of y into equation (3) to get,


[tex]x = 3(2) - 1[/tex]


[tex]x = 5[/tex]