Please assist with the following and show me how you came to

Please assist with the following and show me how you came to your answer. Find the solution to the following system of equations. If the system of equations is inconsistent, please state so.

2x - y = 10

3x + y = 10

Thank you.

Solution

2x - y = 10      ----------->(1)

3x + y = 10      ----------> (2)

To solve the above system of equations we could use either the elimination or the substitution method.

Lets use the Elimination method

Add equations (1) and (2)

=> 5x = 20

so x = 20/5 = 4

we have the x value to find the corresponding y value we could plug x= 2 in any of the two given equaitons and solve for y.

lets plug x = 4 in equation (1)

=> 2x-y = 10

2(4) - y = 10

=> y = -2

hence the system of equations has a unique solutions so this system is consistent in nature

the solution is (4 ,-2)

*Note : consistent if there is at least one set of values for the unknowns that satisfies every equation in the system—that is, that when substituted into each of the equations makes the equation hold true as an identity. In contrast, an equation system is inconsistent if there is no set of values for the unknowns that satisfy all of the equations.