Answer:
The x-coordinate of the intersection point (x, y) = (-0.5, -1) of the system is: -0.5
Hence, option A) i.e. -0.5 is correct.
Step-by-step explanation:
Given the system of equations
2.4x - 1.5y = 0.3
1.6x + 0.5y = -1.3
solving the system of equations
![\begin{bmatrix}2.4x-1.5y=0.3\\ 1.6x+0.5y=-1.3\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D2.4x-1.5y%3D0.3%5C%5C%201.6x%2B0.5y%3D-1.3%5Cend%7Bbmatrix%7D)
Multiply 2.4x - 1.5y = 0.3 by 2
Multiply 1.6x + 0.5y = -1.3 by 3
so the system of equations becomes
![\begin{bmatrix}4.8x-3y=0.6\\ 4.8x+1.5y=-3.9\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D4.8x-3y%3D0.6%5C%5C%204.8x%2B1.5y%3D-3.9%5Cend%7Bbmatrix%7D)
so
![4.8x+1.5y=-3.9](https://tex.z-dn.net/?f=4.8x%2B1.5y%3D-3.9)
![-](https://tex.z-dn.net/?f=-)
![\underline{4.8x-3y=0.6}](https://tex.z-dn.net/?f=%5Cunderline%7B4.8x-3y%3D0.6%7D)
![4.5y=-4.5](https://tex.z-dn.net/?f=4.5y%3D-4.5)
so the system of equations becomes
![\begin{bmatrix}4.8x-3y=0.6\\ 4.5y=-4.5\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D4.8x-3y%3D0.6%5C%5C%204.5y%3D-4.5%5Cend%7Bbmatrix%7D)
solve 4.5y = -4.5 for y
![4.5y=-4.5](https://tex.z-dn.net/?f=4.5y%3D-4.5)
Multiply both sides by 10
![4.5y\cdot \:10=-4.5\cdot \:10](https://tex.z-dn.net/?f=4.5y%5Ccdot%20%5C%3A10%3D-4.5%5Ccdot%20%5C%3A10)
Refine
![45y=-45](https://tex.z-dn.net/?f=45y%3D-45)
Divide both sides by 45
![\frac{45y}{45}=\frac{-45}{45}](https://tex.z-dn.net/?f=%5Cfrac%7B45y%7D%7B45%7D%3D%5Cfrac%7B-45%7D%7B45%7D)
Simplify
![y=-1](https://tex.z-dn.net/?f=y%3D-1)
For 4.8x - 3y = 0.6, plug in y = -1
![4.8x-3\left(-1\right)=0.6](https://tex.z-dn.net/?f=4.8x-3%5Cleft%28-1%5Cright%29%3D0.6)
![4.8x+3\cdot \:1=0.6](https://tex.z-dn.net/?f=4.8x%2B3%5Ccdot%20%5C%3A1%3D0.6)
![4.8x+3=0.6](https://tex.z-dn.net/?f=4.8x%2B3%3D0.6)
Multiply both sides by 10
![4.8x\cdot \:10+3\cdot \:10=0.6\cdot \:10](https://tex.z-dn.net/?f=4.8x%5Ccdot%20%5C%3A10%2B3%5Ccdot%20%5C%3A10%3D0.6%5Ccdot%20%5C%3A10)
Refine
![48x+30=6](https://tex.z-dn.net/?f=48x%2B30%3D6)
Subtract 30 from both sides
![48x+30-30=6-30](https://tex.z-dn.net/?f=48x%2B30-30%3D6-30)
Simplify
![48x=-24](https://tex.z-dn.net/?f=48x%3D-24)
Divide both sides by 48
![\frac{48x}{48}=\frac{-24}{48}](https://tex.z-dn.net/?f=%5Cfrac%7B48x%7D%7B48%7D%3D%5Cfrac%7B-24%7D%7B48%7D)
simplify
![x=-\frac{1}{2}](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B1%7D%7B2%7D)
or
![x = -0.5](https://tex.z-dn.net/?f=x%20%3D%20-0.5)
Thus,
(x, y) = (-0.5, -1)
Therefore, the x-coordinate of the intersection point (x, y) = (-0.5, -1) of the system is: -0.5
Hence, option A) i.e. -0.5 is correct.