solve the system: 2x-5y= 3 x+ 4y = 8
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calendarEducator since 2009
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First, we can say that x = 8 - 4y. Then we can substitute that into the first equation.
Once we have done that, we can make the following new equation:
2 (8 - 4y) - 5y = 3
This becomes
16 - 8y - 5y = 3
By subtracting 16 from both sides, we get
-8y - 5y = -13
or
-13 y = -13
By dividing both sides by -13, we get
y = 1
Now we substitute that back into the first equation and we get
x + 4 = 8
or
x = 4
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
2x-5y = 3...........(1)
x+ 4y = 8............(2)
We will use the substitution method to solve.
Let us rewrite eq. (2):
x+ 4y = 8
==> x= 8-4y
Now substitute x value in eq. (1):
2x-5y = 3
==> 2(8-4y) - 5y = 3
Open brackets:
==> 16 - 8y - 5y = 3
==> -13y = -13
==> y= 1
but x= 8- 4y
==> x= 8- 4*1 = 4
==> x= 4
2x - 5y=3 -------1 x+4y=8
x + 4y = 8 -------2
multiply equation 2 by 2 gives 2(x + 4y) = 8 * 2 2x + 8y = 16
2x - 5y = 3 -------1
2x + 8y = 16 -----3 Subtract 3 from 1 ngives
-5y - 8y = 3 - 16
-13y = -13
y=1
x + 4y = 8
x = 8 - 4y
x = 8 - 4(1)
x = 8 - 4
x = 4
Therefore (x,y) =( 4,1)
2x-5y = 3......(1)
x+4y = 8........(2)
We use the substitution method.
From (2) , we have x = 8-4y. We substitute x = 8-4y in (1):
2(8-4y) - 5y = 3
16 -8y -5y = 3
16 -13y = 3
16-3 = 13y
13 = 13y
13/13 = y
y = 1.
Substitute y = 1 in (1):
2x-5*1 = 3
2x-5 = 3
2x= 3+5 = 8
x = 8/2 = 4
x = 4 and y = 1.
We'll note the equations of the system as:
2x-5y= 3 (1)
x+ 4y = 8 (2)
We'll solve the system using elimination method. For this reason, we'll multiply (2) by -2:
-2x -8y = -16 (3)
Now, we'll add (3) to (1):
2x-5y-2x -8y=3-16
We'll combine and eliminate like terms:
-13y = -13
We'll divide by -13 and we'll get:
y = 1
We'll substitute y in (1):
2x-5y= 3
2x = 3+5
2x = 8
We'll divide by 2:
x = 4
The solution of the system is: {(4,1)}.
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