SOLUTION: Solve each system by substitution or addition, whichever is easier.
52. 2y – x = 3
x = 3y - 5
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Question 165085: Solve each system by substitution or addition, whichever is easier.
52. 2y – x = 3
x = 3y - 5
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm going to use substitution to solve the system.
Start with the given system
Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
Distribute
Combine like terms on the left side
Subtract 5 from both sides
Combine like terms on the right side
Divide both sides by -1 to isolate y
Divide
Now that we know that , we can plug this into to find
Substitute for each
Simplify
So our answer is and which also looks like )
Notice if we graph the two equations (you have to solve for "y" for each equation first), we can see that their intersection is at . So this verifies our answer.
Graph of (red) and (green)
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