Question

{ax+3y=10

kx−3y=6

In the system of equations above, a and k are constants. If the solution to the system is (2,1) , what is the value of a+k ?

Answer 1

By substituting the solution (2, 1) into the system of equations provided, we can solve for a and k, finding a = 7/2 and k = 9/2. Hence, the sum a + k = 8.

Step-by-step explanation:

The student is asking to solve for the constants a and k in a system of linear equations where the solution to the system is given as the point (2, 1). We can substitute these values into the equations to find the values of a and k.

The system of equations given is:

ax + 3y = 10

kx - 3y = 6

Substituting x = 2 and y = 1 into the equations, we get:

a(2) + 3(1) = 10

k(2) - 3(1) = 6

Solving the first equation for a yields a = (10 - 3)/2 = 7/2. Solving the second equation for k yields k = (6 + 3)/2 = 9/2. Therefore, the value of a + k is 7/2 + 9/2 = 8.

Answer 2

a+k =7

Step-by-step explanation:

In the given system of equations, ax + 3y = 10 and kx - 3y = 6, we are told that the solution to the system is (2,1). This means that when we plug the values x = 2 and y = 1 into the equations, we get two true statements.

To find the value of a + k, we can start by plugging the values x = 2 and y = 1 into the first equation to get:

a(2) + 3(1) = 10

Next, we can solve for a by dividing both sides of the equation by 2:

a + 3/2 = 5

a = 5 - 3/2 = 5/2

Next, we can plug the values x = 2 and y = 1 into the second equation to get:

k(2) - 3(1) = 6

Next, we can solve for k by dividing both sides of the equation by 2:

k - 3/2 = 3

k = 3 + 3/2 = 9/2

Finally, we can add the values of a and k to find the value of a + k:

a + k = (5/2) + (9/2) = 14/2 = 7

Therefore, the value of a + k is 7.