Could you please help me with this linear combination? Thank you!
8x-6y=10
4x-5y=3
Of course! To solve this system of linear equations using linear combination, we need to eliminate one of the variables by multiplying the equations by appropriate constants. The goal is to create a new system of equations where one variable will have the same coefficient (but opposite signs) in each equation.
Let's start by multiplying the first equation by 4 and the second equation by 8 to make the coefficients of x in both equations the same:
4(8x-6y) = 4(10)
8(4x-5y) = 8(3)
This simplifies to:
32x - 24y = 40
32x - 40y = 24
Now, subtract the second equation from the first equation to eliminate x:
(32x - 24y) - (32x - 40y) = 40 - 24
Simplifying the equation gives:
-24y + 40y = 40 - 24
16y = 16
Finally, solve for y:
y = 16/16
y = 1
Now substitute the y value back into either original equation. Let's use the first equation:
8x - 6(1) = 10
8x - 6 = 10
8x = 16
x = 16/8
x = 2
So the solution to the system of linear equations is x = 2 and y = 1.