Question

Solve the linear system:

8x+3y=16​
2x-3y=16
(a) x=2,y=4
(b) x=3,y=5
(c) x=4,y=6
(d) x=5,y=7

Answer 1

The solution to the system of linear equations is x = 3.2 and y = -3.2, which does not correspond to any of the multiple choice options provided, suggesting an error in the question or the options.

Step-by-step explanation:

The question involves solving a system of linear equations using algebraic methods. The system given is:

• 8x + 3y = 16
• 2x - 3y = 16

By adding the two equations, we can eliminate the variable y:

1. 8x + 3y + 2x - 3y = 16 + 16
2. (8x + 2x) + (3y - 3y) = 32
3. 10x = 32
4. x = 32/10
5. x = 3.2

Once we have found the value of x, we can substitute it into one of the original equations to solve for y:

1. 8(3.2) + 3y = 16
2. 25.6 + 3y = 16
3. 3y = 16 - 25.6
4. 3y = -9.6
5. y = -9.6/3
6. y = -3.2

Thus, the solution to the system of equations is x = 3.2 and y = -3.2. This solution does not match any of the options given in the question, indicating a possible error in the question or the options provided.