Question

Y = â€"A system of equations. Y equals negative StartFraction one-half EndFraction x plus 4. X plus 2 y equals negative 8. X 4 x 2y = â€"8 How many solutions does this linear system have? one solution: (8, 0) one solution: (0, 8) no solution infinite number of solutions.

Answer 1

For the given system of equation there is no solution.

Given-

The given equation are,

$y=-\dfrac{1}{2} x+4,$

$x+2y=8$

On solving the second equation,

$x+2y=8$

$2y=8-x$

$y=-\dfrac{x}{2}+4$

This is the same equation as equation one with same slope of -1/2.Thus for with the function of y for both equation we get two parallel lines. As parallel lines do not intercept at any point hence we get no solution for the given problem.

Hence, for the given system of equation there is no solution.

For more about the linear equation follow the link below-

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