IDNLearn.com provides a comprehensive solution for all your question and answer needs. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.
Given:
The system of equations is
[tex]8x+9y=36[/tex]
[tex]3x+4y=16[/tex]
To find:
The solution of the given system of equations using the substituting method.
Solution:
We have,
[tex]8x+9y=36[/tex] ...(i)
[tex]3x+4y=16[/tex] ...(ii)
From (ii), we get
[tex]3x=16-4y[/tex]
[tex]x=\dfrac{16-4y}{3}[/tex] ...(iii)
Putting this value in (i), we get
[tex]8\left(\dfrac{16-4y}{3}\right)+9y=36[/tex]
Multiply both sides by 3.
[tex]8(16-4y)+27y=108[/tex]
[tex]128-32y+27y=108[/tex]
[tex]-5y=108-128[/tex]
[tex]y=\dfrac{-20}{-5}[/tex]
[tex]y=4[/tex]
Putting y=4 in (iii), we get
[tex]x=\dfrac{16-4(4)}{3}[/tex]
[tex]x=\dfrac{16-16}{3}[/tex]
[tex]x=\dfrac{0}{3}[/tex]
[tex]x=0[/tex]
Therefore, the solution of given system of equations is (0,0).