Solve the system: x+2y = 5 2x-3y = 2
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calendarEducator since 2009
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If x + 2y = 5, then we can find a value for x by subtracting 2y from both sides. That value is
x = 5 - 2y
Now substitute that in to the second equation.
2 (5 - 2y) -3y = 2
Once we do the math on that, we get
10 - 4y - 3y = 2
10 - 7y = 2
Now we subtract 10 from both sides and we get
-7y = - 8
Divide both sides by -7 and we have
y = 8/7
If y = 8/7
x + 2(8/7) = 5
x + 16/7 = 5
x = 5 - 16/7
x = 35/7 - 16/7
x = 19/7
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
x + 2y = 5........(1)
2x - 3y = 2.......(2)
Using the elimination method:
Multiply (2) by -2 and add to (1)
-7 y = -8
==> y= 8/7
Now substitute:
x + 2y = 5
x = 5 - 2y
= 5 - 2(8/7)
= 5- 16/7
= (35-16)/7
= 19/7
x = 19/7
The set of equations x+2y = 5 and 2x-3y = 2 has to be solved for x and y.
From x + 2y = 5, we get x = 5 - 2y
Substitute this in the second equation 2x - 3y = 2
2*(5 - 2y) - 3y = 2
10 - 4y - 3y = 2
10 - 7y = 2
-7y = -8
y = 8/7
Substitute this in x = 5 - 2y
x = 5 - 2*(8/7)
x = 5 - 16/7
x = (35 - 16)/7 = 19/7
The solution of the set of equations x+2y = 5 and 2x-3y = 2 is x = 19/7 and y = 8/7
Given:
x + 2y = 5 ... (1)
2x - 3y = 2 ... (2)
Multiplying equation (1) by 2:
2x + 4y = 10 ... (3)
Subtracting equation (2) from (3):
2x - 2x + 4y + 3y = 10 - 2
==> 7y = 8
==> y = 8/7
Substituting this value of y in equation (1)
x + 2*(8/7) = 5
==> x + 16/7 = 5
==> x = 5 - 16/7 = 19/7
Answer:
x = 19/7, y = 8/7
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