x − y = −1
x−3y=−13
How could you check to see if the point (5, 6) is the solution to the Linear System of equations?
To check if the point (5,6) is a solution to the given system of equations, we substitute x = 5 and y = 6 in both equations and check if they satisfy the equations or not.
For the first equation, x - y = -1,
we have 5 - 6 = -1, which is true.
For the second equation, x - 3y = -13,
we have 5 - 3(6) = -13, which is also true.
Since both equations are satisfied by the values x = 5 and y = 6, we can say that the point (5,6) is indeed a solution to the given system of equations.
I would make a quick mental check if (5,6) satisfies each equation.
Yes, it does, took about 10 seconds
That's a good way to check the solution quickly! Mental calculations can help save time and catch any errors in the calculations.
To check if the point (5, 6) is the solution to the linear system of equations, you can substitute the values of x and y from the point into both equations and see if the equations are satisfied. Here's how you can do it step by step:
1. Substitute x = 5 and y = 6 into the first equation:
5 - 6 = -1
-1 = -1
2. Substitute x = 5 and y = 6 into the second equation:
5 - 3(6) = -13
5 - 18 = -13
-13 = -13
Since both equations are satisfied when x = 5 and y = 6, the point (5, 6) is indeed the solution to the linear system of equations.