2.4x − 1.5y = 0.3
1.6x + 0.5y = −1.3
The system of equations above is graphed in the xy -plane. What is the x -coordinate of the intersection point (x , y) of the system?

Options

A. `-0.5`
B. `-0.25`
C. `0.8`
D. `1.75`

Answer

A

Explanation

The intersection point (x, y) of the two graphs can be found by multiplying the second equation in the system 1.6x + 0.5y = −1.3 by 3, which gives 4.8x + 1.5y = −3.9. The y-terms in the equation 4.8x + 1.5y = −3.9 and the first equation in the system 2.4x − 1.5y = 0.3 have coefficients that are opposites. Adding the left- and right-hand sides of the equations 4.8x + 1.5y = −3.9 and 2.4x − 1.5y = 0.3 produces 7.2x + 0.0y = −3.6, which is equivalent to 7.2x = −3.6. Dividing both sides of the equation by 7.2 gives x = −0.5. Therefore, the xcoordinate of the intersection point (x, y) of the system is −0.5.
Choice B is incorrect. An x-value of −0.25 produces y-values of −0.6 and −1.8 for each equation in the system, respectively. Since the same ordered pair doesn’t satisfy both equations, neither point can be the intersection point. Choice C is incorrect. An x-value of 0.8 produces y-values of 1.08 and −5.16 for each equation in the system, respectively. Since the same ordered pair doesn’t satisfy both equations, neither point can be the intersection point. Choice D is incorrect. An x-value of 1.75 produces y-values of 2.6 and −8.2 for each equation in the system, respectively. Since the same ordered pair doesn’t satisfy both equations, neither point can be the intersection point.