Graph the system below and write its solution.
=+3xy−6
=y−−12x1
First, fix the typos!
To graph the system of equations, we need to graph each equation separately and find their intersection point(s) which represent the solution(s) to the system.
Equation 1: 3xy - 6
To graph this equation, we can rearrange it to solve for y:
y = 6 - 3xy
We can choose some x-values and substitute them into the equation to find corresponding y-values. Then, we plot these points on a coordinate plane and connect them to form a line.
For example, let's choose x = 0:
y = 6 - 3(0)(y)
y = 6 - 0
y = 6
So, one point on the graph is (0, 6).
Now, let's choose x = 2:
y = 6 - 3(2)(y)
y = 6 - 6y
7y = 6
y = 6/7
Another point on the graph is (2, 6/7).
By repeating this process and connecting the points, we obtain a line.
Equation 2: y - 12x = 1
To graph this equation, let's rearrange it to solve for y:
y = 12x + 1
Again, we can choose some x-values and find the corresponding y-values. We plot these points and connect them to form a line.
For x = 0, y = 12(0) + 1 = 1
So, one point on the graph is (0, 1).
For x = 1, y = 12(1) + 1 = 13
Another point on the graph is (1, 13).
By repeating this process, we obtain a line.
Now, we plot both lines on the same coordinate plane:
By visual inspection, we can find the intersection point of the two lines. This point represents the solution to the system of equations.
In this case, the lines intersect at approximately (1.79, 2.11).
Therefore, the solution to the system of equations is x ≈ 1.79 and y ≈ 2.11.
Note: The values obtained are approximations since we are graphing and estimating the intersection point on a coordinate plane.