May you please show me how to solve this system of equations

4X+5Y=41
3Y+2X=23

Please show step-by-step of how to solve.

There are two ways to do this problem (maybe even more):
-linear combination
-substitution

Linear Combination:
Step 1: multiply one of the equations by a number to make one of the coefficients match
In this case, I will multiply the bottom one by 2.
4X+5Y=41
4X+6Y=46
Step 2: Subtract one equation from the other
4X+5Y=41
-4X-6Y=-46
-----------------
-1Y=-5

Step 3: solve for Y

Y = 5

Step 4: plug Y into one of the original equations

4X+5Y=41
4X+5(5)=41

Step 5: Solve for X

4X + 25 = 41
4X = 16
X = 4

Therefore, Y =5, X = 4

Substitution:

Step 1: isolate one variable
in this case, we will isolate x first (does not matter which though)

4X + 5Y = 41
4X = -5Y + 41
X = (-5Y + 41) / 4

Step 2: substitute this equation of X into the the opposite equation used

4X + 6Y = 46
4 ((-5Y + 41) / 4) + 6Y = 46

Step 3: Solve for Y

-5Y + 41 + 6Y = 46
Y + 41 = 46
Y = 5

Step 4: Plug in value for Y into an original equation

4X + 5Y = 41
4X + 5(5) = 41
4X + 25 = 41
4X = 16
X = 4

Therefore, Y = 5, X = 4

get rid of one of the variables
so multiply bottom by -2
4x + 5y = 41
-4x -6y = -46

add together
0 -y = -5
y = 5
x = 4