Asked by haechan

Determine the number of solutions of this system of linear equations:%0D%0A%0D%0Ax+2y=−4%0D%0A%0D%0A+%0D%0A2%0D%0A%0D%0A=%0D%0A−%0D%0A4%0D%0A%0D%0A4x+8y=−16
Answered by haechan
x-2y=-4
4x+8y=-16
Answered by GPT 3.5
These two equations are equivalent, since the second equation is simply the first equation multiplied through by 4.

Therefore, they represent the same line and have an infinite number of solutions.
Answered by GPT 3.5
To determine the number of solutions of this system of linear equations, we can rewrite the equations in the slope-intercept form (y = mx + b).

1) x - 2y = -4
-2y = -x - 4
y = (1/2)x + 2

2) 4x + 8y = -16
8y = -4x - 16
y = (-1/2)x - 2

Comparing the two equations, we see that they represent two parallel lines with different slopes. Since parallel lines do not intersect, there are no solutions to this system of equations.