Answer:
x − 4x + 6y + (14x − 5y) ⇔ 11x+y
(5x − 3y) − x + 3x − 5y ⇔ 7x-8y
5(x + y) + 6(x − y) ⇔ 11x-y
3x + 3y + 2(2x − y) ⇔ 7x+y
Step-by-step explanation:
Solve the following;
3x + 3y + 2(2x − y)
4(x + y) − 3(x + y)
x − 4x + 6y + (14x − 5y)
(5x − 3y) − x + 3x − 5y
5(x + y) + 6(x − y)
Solve:
3x + 3y + 2(2x − y)
[tex]=3x+3y+4x-2y[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=3x+4x+3y-2y[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:3x+4x=7x[/tex]
[tex]=7x+3y-2y[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:3y-2y=y[/tex]
[tex]=7x+y[/tex]
Hence, this tiles will be used.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4(x + y) − 3(x + y)
[tex]\mathrm{Add\:similar\:elements:}\:4\left(x+y\right)-3\left(x+y\right)=\left(x+y\right)[/tex]
[tex]=x+y[/tex]
Thus, this tiles will not be used.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
x − 4x + 6y + (14x − 5y)
[tex]\mathrm{Apply\:rule}:\quad \:a+\left(b+c\right)=a+b+c[/tex]
[tex]6y+\left(14x-5y\right)=6y+14x-5y[/tex]
[tex]=x-4x+6y+14x-5y[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=x-4x+14x+6y-5y[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:x-4x+14x=11x[/tex]
[tex]=11x+6y-5y[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:6y-5y=y[/tex]
[tex]=11x+y[/tex]
Thus, this tiles will be used
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(5x − 3y) − x + 3x − 5y
[tex]\mathrm{Apply\:rule}:\quad \left(a\right)=a[/tex]
[tex]\left(5x-3y\right)=5x-3y[/tex]
[tex]=5x-3y-x+3x-5y[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=5x-x+3x-3y-5y[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:5x-x+3x=7x[/tex]
[tex]=7x-3y-5y[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:-3y-5y=-8y[/tex]
[tex]=7x-8y[/tex]
Hence, this tiles will be used
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
5(x + y) + 6(x − y)
[tex]=5x+5y+6\left(x-y\right)[/tex]
[tex]=5x+5y+6x-6y[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=5x+6x+5y-6y[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:5x+6x=11x[/tex]
[tex]=11x+5y-6y[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:5y-6y=-y[/tex]
[tex]=11x-y[/tex]
Hence, this tiles will be used
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