Answer:
(x, y) = (1, 2)
Explanation:
You want to solve the system of equations x=2y-3, -4x+3y=2 using the substitution method.
Substitution
The first equation gives you an expression for x that can be substituted into the second equation.
-4(2y-3) +3y = 2 . . . . . . substitute (2y-3) for x
-8y +12 +3y = 2 . . . . . simplify
10 = 5y . . . . . . . . . . add 5y -2 to both sides
2 = y . . . . . . . . . . divide by 5
Now, the value of x can be found from the first equation:
x = 2(2)-3 = 1
The solution is (x, y) = (1, 2).
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Additional comment
The advantage of the substitution method is that once you find the value of the remaining variable, you can use the substitution equation to find the value of the variable that was eliminated. That is, the equation for x made it easy to find x once we solved for y.
Substitution is easiest when there is already an equation for one of the variables. It can also be used fairly easily if one of the variables has a coefficient of 1 or -1.