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
[tex]\begin{bmatrix}2.4x-1.5y=0.3\\ 1.6x+0.5y=-1.3\end{bmatrix}[/tex]
Multiply 2.4x - 1.5y = 0.3 by 2
Multiply 1.6x + 0.5y = -1.3 by 3
so the system of equations becomes
[tex]\begin{bmatrix}4.8x-3y=0.6\\ 4.8x+1.5y=-3.9\end{bmatrix}[/tex]
so
[tex]4.8x+1.5y=-3.9[/tex]
[tex]-[/tex]
[tex]\underline{4.8x-3y=0.6}[/tex]
[tex]4.5y=-4.5[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}4.8x-3y=0.6\\ 4.5y=-4.5\end{bmatrix}[/tex]
solve 4.5y = -4.5 for y
[tex]4.5y=-4.5[/tex]
Multiply both sides by 10
[tex]4.5y\cdot \:10=-4.5\cdot \:10[/tex]
Refine
[tex]45y=-45[/tex]
Divide both sides by 45
[tex]\frac{45y}{45}=\frac{-45}{45}[/tex]
Simplify
[tex]y=-1[/tex]
For 4.8x - 3y = 0.6, plug in y = -1
[tex]4.8x-3\left(-1\right)=0.6[/tex]
[tex]4.8x+3\cdot \:1=0.6[/tex]
[tex]4.8x+3=0.6[/tex]
Multiply both sides by 10
[tex]4.8x\cdot \:10+3\cdot \:10=0.6\cdot \:10[/tex]
Refine
[tex]48x+30=6[/tex]
Subtract 30 from both sides
[tex]48x+30-30=6-30[/tex]
Simplify
[tex]48x=-24[/tex]
Divide both sides by 48
[tex]\frac{48x}{48}=\frac{-24}{48}[/tex]
simplify
[tex]x=-\frac{1}{2}[/tex]
or
[tex]x = -0.5[/tex]
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.
