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.

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(52788)   (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.

RELATED QUESTIONS
what is the slope of the line represented by the equation... (answered by rfer)
Which choice is the equation of a line that passes through the point (�2, 8) and is... (answered by Theo)
which equation represents a line that is paralle to the line represented by the equation... (answered by Alan3354)
what is the slope of a line that is parallel to the line represented by the equation... (answered by J2R2R)
Which equation produces a line that is perpendicular to the line represented by the... (answered by jim_thompson5910)
Which equation produces a line that is perpendicular to the line represented by the... (answered by Fombitz)
What is the slope of a line that is parallel to the line represented by the equation... (answered by richard1234,Alan3354)
What is the slope of the line represented by the equation -2y = x -... (answered by flame8855)
Line Q is represented by the following equation: 2x + y = 11 Which equation completes (answered by solver91311)