The perimeter of parallelogram WXYZ is 22
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The required system of equations is ![x+y=5\\x-y=-3](https://tex.z-dn.net/?f=x%2By%3D5%5C%5Cx-y%3D-3)
Step-by-step explanation:
We need to write a system of linear equations that has the ordered pair (1,4) as it's solution.
It means we need to find system of linear equations, which after being solved gives x=1 and y=4
Let the system of equations be:
![x+y=5\\x-y=-3](https://tex.z-dn.net/?f=x%2By%3D5%5C%5Cx-y%3D-3)
I have made equations such that adding x+y gives 5 i,e (1+4=5) and subtracting x-y gives -3 (1-4=-3)
Now solving this system of equations to find value of x:
![x+y=5\,\,eq(1)\\x-y=-3\,\,eq(2)](https://tex.z-dn.net/?f=x%2By%3D5%5C%2C%5C%2Ceq%281%29%5C%5Cx-y%3D-3%5C%2C%5C%2Ceq%282%29)
Adding eq(1) and eq(2)
![x+y=5\\x-y=-3\\-----\\2x=2\\x=1](https://tex.z-dn.net/?f=x%2By%3D5%5C%5Cx-y%3D-3%5C%5C-----%5C%5C2x%3D2%5C%5Cx%3D1)
Putting value of x=1 into eq(1) to find value of y
![x+y=5\\1+y=5\\y=5-1\\y=4](https://tex.z-dn.net/?f=x%2By%3D5%5C%5C1%2By%3D5%5C%5Cy%3D5-1%5C%5Cy%3D4)
The solution set after solving system of equations is (1,4).
The required system of equations is ![x+y=5\\x-y=-3](https://tex.z-dn.net/?f=x%2By%3D5%5C%5Cx-y%3D-3)
Keywords: System of equations
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