Answer:
(x, y) = (4, -3)
Explanation:
You want to solve this system of equations using substitution.
Substitution
The substitution method requires that you find an expression for one of the variables that you can use to replace that variable in the other equation.
Here, we choose to use the second equation to write an expression for y. This makes the resulting coefficients be decimal values.
5y = 9 -6x . . . . subtract 6x
y = 1.8 -1.2x . . . . divide by 5
Substituting this for y in the first equation gives ...
4x -3(1.8 -1.2x) = 25
7.6x -5.4 = 25 . . . . . . . simplify
7.6x = 30.4 . . . . . . . . add 5.4
x = 4 . . . . . . . . . . divide by 7.6
y = 1.8 -1.2(4) = 1.8 -4.8
y = -3
The solution is (x, y) = (4, -3).
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Additional comment
We could have used the first equation to write an expression for x. That would also make the coefficients be terminating decimal values. Using the first equation to write an expression for y leaves coefficients that are multiples of 1/3, not nice decimals. Similarly, solving the second equation for x would result in coefficients that are multiples of 1/6, also not nice decimals.
These "not nice" values can be used to get the same result. It just depends on what kind of arithmetic you want to do: fractions or decimals.
This set of coefficients would generally indicate that some other method would be more desirable to use: graphing, or matrix methods, for example. The attachment shows a matrix method.