Question

The solution of the system 4x+5y=2 and 6x-2y=b is (3,a). Find the values of a and b.

Answer 1

To find the values of a and b in the given system of equations, solve for x in terms of y from the first equation, substitute it into the second equation, and solve for a and b. The values of a and b are -2 and 12, respectively.

Step-by-step explanation:

To find the values of a and b in the given system of equations, we can use substitution. We start with the first equation:

4x + 5y = 2

From this equation, we can isolate x by subtracting 5y from both sides:

4x = 2 - 5y

Dividing both sides by 4, we get:

x = (2 - 5y)/4

Next, we substitute this value of x into the second equation:

6x - 2y = b

Replacing x with (2 - 5y)/4, we get:

6((2 - 5y)/4) - 2y = b

Simplifying the equation:

(12 - 30y)/4 - 2y = b

Multiplying both sides by 4 to get rid of the denominator:

12 - 30y - 8y = 4b

Combining like terms:

12 - 38y = 4b

To find a, we substitute the value x = 3 into the first equation:

4(3) + 5y = 2

Simplifying the equation:

12 + 5y = 2

Subtracting 12 from both sides:

5y = -10

Dividing by 5:

y = -2

Hence, the solution is (3,-2) and the values of a and b are -2 and 12, respectively.

Answer 2

Plug x=3 in the first equation to find y:
4(3)+5y=2
y=-2
so a=-2

Next, plug x=3, y=-2 in the second equation to find b:
6(3)-2(-2)=22
b=22