Billy graphed the system of linear equations to find an approximate solution. y = A system of equations. y equals negative Start
Fraction 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)
2 answers:
Response:
Second option:
Third option:
Detailed explanation:
The missing graph has been provided.
The attached image illustrates the graphing of the following system of linear equations:
Notice the intersection of the lines.
According to the definition, if lines in a system of equations intersect, then there is only one solution. This implies that the intersection point is the solution to that system. This can be expressed as:
Represented by "x" for the x-coordinate and "y" for the y-coordinate.
Here, it's noticeable that:
- The x-coordinate of the intersection point lies between and
.
- The y-coordinate of the intersection point is situated between and
.
Therefore, you can conclude that the forthcoming points (Refer to the options given in the exercise) are potential approximations for this system:
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Answer: x1 = 251/26, x2 = -111/26
Step-by-step explanation:
Greetings!
As illustrated in the diagram, the point you seek is where the two lines intersect.
This intersection point is found by solving the system of linear equations (both equations must be satisfied by the point):
You can approach solving it using the substitution method:
Then substitute x1 into equation 2 to resolve x2:
After which, utilize the x2 value to establish x1:
