Respuesta :
Answer:
Option d) 4x + 2y = 10 and 8x = 16 is correct
Therefore 4x + 2y = 10 and 8x = 16 equations have equivalent solution (2,1) is same as the solution of given linear system of equations
Step-by-step explanation:
Given equations are
[tex]4x-2y=6\hfill (1)[/tex]
[tex]2x+y=5\hfill (2)[/tex]
To find the the equivalent system of linear equations that will produce the same solution as for the given equation :
First find the solution to the given system of equations by elimination method
Multiply the equation (2) into 2 we get
[tex]4x+2y=10\hfill (3)[/tex]
Now adding the equations (1) and ( 3) we get
[tex]4x-2y=6[/tex]
[tex]4x+2y=10[/tex]
_______________
[tex]8x=16[/tex]
[tex]x=\frac{16}{8}[/tex]
x=2
Therefore the value of x is 2
Substitute the value of x in equation (1) we get
[tex]4(2)-2y=6[/tex]
[tex]8-2y=6[/tex]
[tex]-2y=6-8[/tex]
[tex]-2y=-2[/tex]
[tex]y=\frac{-2}{-2}[/tex]
y=1
Therefore the value of y is 1
Therefore the solution to the given system of equations is (2,1)
Now to find the equivalent system of equations have same solution (2,1)
Verify the equations [tex]4x+2y=10\hfill (4)[/tex] and 8x = 16
From 8x=16
[tex]x=\frac{16}{8}[/tex]
x=2
Therefore the value of x is 2
Substitute x=2 in equation (4) we get
4(2)+2y=10
8+2y=10
2y=10-8
2y=2
[tex]y=\frac{2}{2}[/tex]
y=1
Therefore the value of y is 1
Therefore the solution is (2,1)
