Does the graph (-2, 6) intersect at x+2y=10 and 3x+y=0
To determine if the point (-2, 6) lies on the graphs of the equations x + 2y = 10 and 3x + y = 0, we can substitute the x and y values of the point into each equation and check if the equation is satisfied.
For the equation x + 2y = 10:
(-2) + 2(6) = 10
-2 + 12 = 10
10 = 10
The equation is satisfied for the first equation.
For the equation 3x + y = 0:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
The equation is also satisfied for the second equation.
Therefore, the point (-2, 6) satisfies both equations and thus intersects both graphs.
To check if the point (-2, 6) lies on the lines x + 2y = 10 and 3x + y = 0, we need to substitute the x and y values into the equations and see if they satisfy the equations.
For the equation x + 2y = 10:
Substituting x = -2 and y = 6:
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
The equation is satisfied, so the point (-2, 6) lies on the line x + 2y = 10.
Now, let's check for the line 3x + y = 0:
Substituting x = -2 and y = 6:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
The equation is also satisfied, so the point (-2, 6) lies on the line 3x + y = 0.
Therefore, the graph (-2, 6) intersects at x + 2y = 10 and 3x + y = 0.
To determine whether the point (-2, 6) lies on the intersection of the lines x + 2y = 10 and 3x + y = 0, we can substitute the x and y coordinates of the point into the equations and check if they satisfy both equations.
Let's start with the first equation, x + 2y = 10:
Substituting x = -2 and y = 6 into the equation:
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
The result of this equation is true.
Now, let's move on to the second equation, 3x + y = 0:
Substituting x = -2 and y = 6 into the equation:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
The result of this equation is also true.
Since (-2, 6) satisfies both equations, it lies on the intersection of the lines x + 2y = 10 and 3x + y = 0.