Which ordered pair represents the solution to the system of equations?{2x−7y=0x−6y=-5{2𝑥-7𝑦=0𝑥-6𝑦=-5 (1, 1) (2, 7) (7, 2) (-11, -1)
Question
Which ordered pair represents the solution to the system of equations?{2x−7y=0x−6y=-5{2𝑥-7𝑦=0𝑥-6𝑦=-5 (1, 1) (2, 7) (7, 2) (-11, -1)
Solution
The solution to the system of equations can be found by either substitution or elimination method. Let's use the substitution method:
The system of equations is:
2x - 7y = 0 x - 6y = -5
From the first equation, we can express x in terms of y:
x = 7y/2
Substitute x = 7y/2 into the second equation:
7y/2 - 6y = -5 Multiply all terms by 2 to get rid of the fraction:
7y - 12y = -10 Combine like terms:
-5y = -10 Divide by -5:
y = 2
Substitute y = 2 into the first equation:
2x - 7*2 = 0 2x - 14 = 0 Add 14 to both sides:
2x = 14 Divide by 2:
x = 7
So, the solution to the system of equations is (7, 2).
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