Option D: [tex]x=3,y=-2[/tex] is the solution to the system of equations.
Explanation:
Given that the equations are [tex]4x+y=10[/tex] and [tex]2x+y=4[/tex]
We need to determine the solution of the system of equations.
The solution can be determined by solving the two equations.
Let us solve the system of equations using substitution method.
Consider the equation [tex]4x+y=10[/tex] , the value of y is given by
[tex]y=10-4x[/tex]
Substituting the value of [tex]y=10-4x[/tex] in the equation [tex]2x+y=4[/tex] , we get,
[tex]2x+(10-4x)=4[/tex]
Simplifying, we get,
[tex]2x+10-4x=4[/tex]
[tex]-2x+10=4[/tex]
[tex]-2x=-6[/tex]
[tex]x=3[/tex]
Substituting the value of [tex]x=3[/tex] in [tex]4x+y=10[/tex] , we get,
[tex]4(3)+y=10[/tex]
[tex]12+y=10[/tex]
[tex]y=-2[/tex]
Thus, the solution to the system of equations is [tex]x=3,y=-2[/tex]
Hence, Option D is the correct answer.
