Two equations that would have a solution of (3,6)

Linear equation is the equation in which the highest power of the unknown variable is 1.The two equations that would have a solution of (3,6) are,

[tex]y=2x[/tex]

[tex]y=-x+9[/tex]

Given information-

The solution of the equation are (3,6).

Linear system of the equation-

In the linear system of the equation there can be three possible solutions as,

One solution
Infinite many solution
No solution

As in the given problem the one solution of the two equation are given (3,6).

It is known that when two lines intersect each other at a point, there is a one unique solution for the two lines.

Suppose the two equation of the line in terms of variable x and y is,

[tex]y=2x[/tex]

[tex]y=-x+9[/tex]

Check this line if the solution of these two line is (3,6) or not,

Put the value of the equation 1 in the equation 2. Thus,

[tex]\begin{aligned}\\2x&=-x+9\\2x+x&=9\\3x&=9\\x&=3\\\end[/tex]

Put this value of x in the equation 1,

[tex]y=2\times 3\\ y=6[/tex]

Thus the equation has solution (3,6).

Hence the two equations that would have a solution of (3,6) are,

[tex]y=2x[/tex]

[tex]y=-x+9[/tex]

Learn more about the linear system here;

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