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Answer:
(x, y) = (3, 12)
Explanation:
The first step in any problem solving is to look at the problem. Here, we see that the first equation can be reduced to standard form by dividing it by 2. This would give both terms a coefficient of 1.
We see that the second equation already has a variable with a coefficient of 1.
When solving a system by substitution, it can save some effort if you start by finding a variable with a coefficient of 1 or -1. Since we see that in the second equation, we choose to solve the second equation for y:
y = 4x . . . . . . . add 4x to both sides of the second equation
Now, we have an expression for y that we can substitute into the first equation.
2x +2(4x) = 30 . . . . substitute for y
10x = 30 . . . . . . . . simplify
x = 3 . . . . . . . . . . divde by 10
y = 4(3) = 12 . . . . . find y using y=4x
The solution is (x, y) = (3, 12).
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Additional comment
I doesn't matter what variable gets substituted. The purpose of the exercise is to reduce the number of variables in the equation. Here, we start with an equation that has 2 variables. Substituting for one of them gives an equation with only one variable, a lot easier to solve.
You don't have to find an expression for the "bare" variable. We could solve the second equation for 2x, for example: 2x = y/2, then substitute for 2x in the first equation: y/2 +2y = 30 ⇒ y = (2/5)(30) = 12. Or, we could solve the first equation for 2x and substitute into the second: 2x=30-2y, y-2(2x) = 0 ⇒ y-2(30-2y) = 0 ⇒ y = 60/5 = 12.
The substitution property of equality says you can make any substitution of equal values anywhere. "butter = margarine" means you can substitute butter for margarine, or vice versa, wherever you may wish.