Q:

Billy graphed the system of linear equations to find an approximate solution. y = A system of equations. y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction. y equals StartFraction 3 over 4 EndFraction x minus 3.x + y = x – 3 A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction and passes through the (0, 2.5) and (2.2, negative 1.4). The second line is labeled y equals StartFraction 3 over 4 EndFraction x minus 3 and passes through (0, negative 3, 0.14) and (2.2, negative 1.4) Which points are possible approximations for this system? Select two options. (1.9, 2.5) (2.2, –1.4) (2.2, –1.35) (1.9, 2,2) (1.9, 1.5)

Accepted Solution

A:
Answer: Second option: [tex](2.2, -1.4)[/tex] Third option: [tex](2.2, -1.35)[/tex]Step-by-step explanation: The missing graph is attached. You can observe in the picture attached that the following system of linear equations is graphed: [tex]\left \{ {{y=-\frac{7}{4}x+\frac{5}{2}} \atop {y=\frac{3}{4}x-3}} \right.[/tex] Notice that the lines intersect each other. By definition, if the lines of the system of equations intersect, then the system have one solution. This means that the point of intersection of the lines is the solution of the system. It can be written as: [tex](x,y)[/tex] Being "x" the x-coordinate and "y" the y-coordinate. In this case you can identify that: - The x-coordinate of the point of intersection is between  [tex]x=2[/tex] and [tex]x=3[/tex]. - The y-coordinate of the point of intersection is between  [tex]y=-1[/tex] and [tex]y=-2[/tex]. Based on this, you can conclude that the following points (See the options provided in the exercise) are possible approximations for this system: [tex](2.2, -1.4)\\\\\\(2.2, -1.35)[/tex]