To solve the system of linear equations 7x + 2y = 6 and 8x + y = 3, we can use the substitution or elimination method. Here, we’ll use the elimination method for clarity.
First, let’s rewrite the equations:
- 1) 7x + 2y = 6
- 2) 8x + y = 3
Next, we want to eliminate one of the variables by aligning the coefficients. We can multiply the second equation by 2 to easily eliminate y:
2(8x + y) = 2(3)
This gives us:
- 3) 16x + 2y = 6
Now, we can subtract equation 1 from equation 3:
(16x + 2y) – (7x + 2y) = 6 – 6
This simplifies to:
9x = 0
Dividing both sides by 9 gives us:
x = 0
Now that we have the value of x, we can substitute it back into one of the original equations to find y. Let’s use equation 2:
8(0) + y = 3
This simplifies to:
y = 3
So, the solution to the system of equations is:
- x = 0
- y = 3
In conclusion, the solution to the system of linear equations 7x + 2y = 6 and 8x + y = 3 is:
(x, y) = (0, 3)