solve the system

Question

2x+3y=9

x-2y=8

Solve for x and y for the following two equations please.And please do step by step so i can get a better understanding.

Answer 1

The two common methods for solving a system of two equations are:

Substitution

Elimination

1. Use Substitution

Solve one equation for one of the variables and substitute that expression into the other equation.

Then, use either equation to solve for the other variable.

For this system of equations, it is easy to solve for x in the second equation:

2x+3y=9

x-2y=8

x = 2y+8

then, substitute for y in the first equation:

2(2y+8) + 3y = 9

7y + 16 = 9

7y = -7

y = -1

Now, use either equation to find x:

x - 2(-1) = 8

x = 6

Check:

Does 2(6)+3(-1)=9 ?

9 = 9 ??? YES

2. Use Elimination (make a coefficient match or opposite]

2x + 3y = 9

2x - 4y = 16 [twice second equation]

----------------------- [elimination; subtract second equation]

7y = -7

y = -1

Now, use either substitution or elimination to find x:

x - 2(-1) = 8

x = 6

Check:

Does 2(6)+3(-1)=9 ?

9 = 9 ??? YES