solve the system of linier equations by A) Substitution, B) elimination

[tex]5x + y = 10 \\ 2x - 6y = 4[/tex]
let's start with substitution. we will solve for one variable using one equation and then substitute j to the other equation. for example let's take the first equation and solve for y
[tex]y = 10 - 5x[/tex]
now put this I to second formula
[tex]2x - 6(10 - 5x) = 4 \\ 2x - 60 + 30x = 4 \\ 32x = 64 \\ x = 2[/tex]
now put this back into first equation
[tex]5(2) + y = 10 \\ 10 + y = 10 \\ y = 0[/tex]
so we get x is 2 and y is 0

now we will save using elimination. to do this we wi multiply one equation so that we can add both equations and cancel out a variable
we will multiply the first equation. by 6
[tex]6(5x + y = 10) \\ 30x + 6y = 60[/tex]
now we will add the two equations
[tex] 30x + 6y = 60\\ + 2x - 6y = 4 \\ 32x = 64 \\ x = 2[/tex]
you can do the same thing and cancel out x to find y.