Solve the following system using the substitution method2y +5x = 104y + 10x = 2
Accepted Solution
A:
Answer: The given system of equations has no solution
Explanation: The first given equation is: 2y + 5x = 10 This can be rewritten as: 2y = 10 - 5x ...............> equation I The second given equation is: 4y + 10x = 2 This can be rewritten as: 2(2y) + 10x = 2 ................> equation II
Substitute with I in II and solve as follows: 2(2y) + 10x = 2 2(10-5x) + 10x = 2 20 - 10x + 10x = 2 20 = 2 Since this is impossible, therefore, the system of equations has no solutions. This means that there is no (x,y) point that would satisfy both equations.
Graphing check: The attached image shows the graphs of the two given functions. We can note that the two lines are parallel each with slope -5/2, which means that they NEVER intersect. Hence, there is no solution for the given system.