<u>QUESTION 1</u>
The given system of equation is
![y=x-6...eqn1](https://tex.z-dn.net/?f=y%3Dx-6...eqn1)
and
![3x+2y=8...eqn2](https://tex.z-dn.net/?f=3x%2B2y%3D8...eqn2)
Let us substitute equation (1) into equation (2) to get,
![3x+2(x-6)=8](https://tex.z-dn.net/?f=3x%2B2%28x-6%29%3D8)
We expand the bracket to get,
![3x+2x-12=8](https://tex.z-dn.net/?f=3x%2B2x-12%3D8)
We simplify to get.
![5x-12=8](https://tex.z-dn.net/?f=5x-12%3D8)
We group like terms to get
![5x=8+12](https://tex.z-dn.net/?f=5x%3D8%2B12)
![\Rightarrow 5x=20](https://tex.z-dn.net/?f=%5CRightarrow%205x%3D20)
![\Rightarrow x=4](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D4)
We now substitute
in to equation (1) to obtain,
![y=4-6=-2](https://tex.z-dn.net/?f=y%3D4-6%3D-2)
The correct answer is option A.
<u>QUESTION 2</u>
The given system of equations is
![y-x=9...eqn1](https://tex.z-dn.net/?f=y-x%3D9...eqn1)
and
![10+2x=-2y...eqn2](https://tex.z-dn.net/?f=10%2B2x%3D-2y...eqn2)
We make y the subject in equation (2) to get,
![y=-x-5..eqn3](https://tex.z-dn.net/?f=y%3D-x-5..eqn3)
We put equation (3) into equation (1) to obtain,
![-x-5-x=9](https://tex.z-dn.net/?f=-x-5-x%3D9)
We group like terms to get,
![-x-x=9+5](https://tex.z-dn.net/?f=-x-x%3D9%2B5)
This implies that,
![-2x=14](https://tex.z-dn.net/?f=-2x%3D14)
We divide through by
to get,
![x=-7](https://tex.z-dn.net/?f=x%3D-7)
Hence the x-coordinate is ![-7](https://tex.z-dn.net/?f=-7)
<u>QUESTION 3</u>
The given system is
![y=3x-1..eqn1](https://tex.z-dn.net/?f=y%3D3x-1..eqn1)
and
![x-y=-9...eqn2](https://tex.z-dn.net/?f=x-y%3D-9...eqn2)
We make
the subject in equation (2) to get,
![x=y-9...eqn3](https://tex.z-dn.net/?f=x%3Dy-9...eqn3)
We put equation (3) into equation (1) to obtain,
![y=3(y-9)-1](https://tex.z-dn.net/?f=y%3D3%28y-9%29-1)
We expand the bracket to get,
![y=3y-27-1](https://tex.z-dn.net/?f=y%3D3y-27-1)
Group like terms to get,
![y-3y=-27-1](https://tex.z-dn.net/?f=y-3y%3D-27-1)
We simplify to get;
![-2y=-28](https://tex.z-dn.net/?f=-2y%3D-28)
This implies that,
![y=14](https://tex.z-dn.net/?f=y%3D14)
Therefore the y-coordinate is 14.