Question

How many solutions does this linear system have? one solution: (0, 0) one solution: (1, –4) no solution infinite number of solutions.

Answer 1

The system of equations has infinite solutions.

Given to us,

• $y=-6x+2$
• $-12x-2y=-4$

Equation 2,

The value of y is already given in equation 1,

$-12x-2y=-4$

substituting the value of y in equation 2,

$-12x-2(-6x+2)=-4\\-12x +12x-4=-4\\-12x+12x=-4+4\\0=0$

The solution of the two equations is 0. Also, we can see that both the equations are in ratio.

Further, the image also shows that the line of the two equations are coinciding.

Hence, the system of equations has infinite solutions.

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