SOLUTION: Line m is represented by the equation 2x + 5y =13 and line n is represented by the equation 5x - 2y =-11. Verify that the point of intersection is a solution to both equations.

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Question 1161021: Line m is represented by the equation 2x + 5y =13 and line n is represented by the equation 5x - 2y =-11. Verify that the point of intersection is a solution to both equations.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
the two equations are:
2x + 5y = 13
5x - 2y = -11
multiply both sides of the first equation by 5 and both sides of the second equation by 2 to get:
10x + 25y = 65
10x - 4y = -22
subtract the second equation from the first to get:
29y = 87
solve for y to get:
y = 87 / 29 = 3
replace y in either original equation with 3 to get:
2x + 15 = 13
solve for x to get:
x = -2/2 = -1
you have a common solution to both equations equal to x = -1 and y = 3
that's the coordinate point (x,y) = (-1,3) on a graph.
the graph looks like this:

you can see from the graph that the intersection point is (-1,3).

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.

It is   by the definition   the intersection point of two lines, given by their equations, is the solution to both equations.

So, there is nothing to check in this problem :   it is TRUE by the definition.