The best approximation for the solution of the system of equations is (0.88,0.65).
Given a system of equations is y=-(2/5)x+1 and y=3x-2.
A system of linear equations consists of two or more equations, and one attempts to solve the equations together.
To find the best approximation solution solve the system of equations.
The given system of equations are
y=-(2/5)x+1 .......(1)
y=3x-2 .......(2)
Firstly, substitute the value of y into equation (1) to find the value of x, we get
3x-2=-(2/5)x+1
Now, we will add (2/5)x in both sides, we get
3x-2+(2/5)x=-(2/5)x+1+(2/5)x
3x-2+(2/5)x=1
Further, we will add 2 on both sides, we get
3x-2+(2/5)x+2=1+2
3x+(2/5)x=3
17x/5=3
Furthermore, we will multiply both sides with 5, we get
5×(17x/5)=3×5
17x=15
Now, divide both sides with 17, we get
17x/17=15/17
x=0.88
Further, we will find the value of y by substituting the value of x in equation (2), we get
y=3(0.88)-2
y=2.65-2
y=0.65
Hence, the best approximation for the solution of the system of equations y=-(2/5)x+1 and y=3x-2 is (0.88,0.65).
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