The given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.
In the question, we are asked for the ordered pair, which is the solution to the system of equations:
2x + 3y= 6 ... (i)
–3x + 5y = 10 ... (ii).
To solve for the solution to the system of equations, we use the elimination method.
We multiply (i) by 3, and (ii) by 2, and then add the resultant equations to eliminate x as follows:
6x + 9y = 18 {(i) * 3}
-6x + 10y = 20 {(ii) * 2}
_____________
19y = 38,
or, y = 38/19 = 2.
Substituting, y = 2, in (i), we get:
2x + 3y = 6,
or, 2x + 3(2) = 6,
or, 2x + 6 = 6,
or, 2x = 6 - 6 = 0,
or, x = 0/2 = 0.
Thus, the given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.
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The complete question is:
"Which ordered pair is a solution to the system of linear equations?
2x + 3y= 6
–3x + 5y = 10
(0,2)
(2,0)
(3,2)
(2,3)"
