Question 335143
You have 2 equations in 2 unknowns.


You want to substitute for one of the variables to get one equation in one unknown.


At least that's what I think you're asking.


Take the first equation and solve for x or y.  


We'll do y.


You start with 3x - y = 5


Add y to both sides of this equation and subtract 5 from both sides of this equation to get:


y = 3x - 5


Substitute for y in the second equation.


The second equation is -4x + 2y = -6


Substitute for y in the second equation by the value of y that you solved for in the first equation to get:


-4x + 2 * (3x-5) = -6


Simplify this by multiplying out the factors to get:


-4x + 6x - 10 = -6


Add 10 to both sides of this equation and combine like terms to get:


2x = 4


Divide both sides of this equation by 2 to get:


x = 2


Now that you know the value of x, you can solve for  y in either of the original 2 equations.


From the first equation,  you have 3x - y = 5


Substitute for x in this equation to get:


3*2 - y = 5 which becomes:


6 - y = 5


Subtract 6 from both sides of this equation to get:


-y = -1


Multiply both sides of this equation by -1 to get:


y = 1


You now have:


x = 2 and y = 1


Substitute in both original equations to see if they are true.


3x - y = 5 becomes 3*2 - 1 = 5 which becomes 6 - 1 = 5 which becomes 5 = 5 which is true.


-4x + 2y = -6 becomes -4*2 + 2*1 = -6 which becomes -8 + 2 = -6 which becomes -6 = -6 which is true.


Both original equations are true, so the values of x = 2 and y = 1 are good.