how much solutions are in the linear equations x +2y = -4 and 4x + 8y = -16
3 answers
The two linear equations x + 2y = -4 and 4x + 8y = -16 represent the same line. This means that the two equations are dependent and have an infinite number of solutions.
explain how you got the answer.
To determine if two linear equations have a unique solution, no solution, or infinite solutions, we can look at their slopes and y-intercepts.
The given equations are:
1) x + 2y = -4
2) 4x + 8y = -16
We can rearrange equation 1 to find the slope-intercept form:
1) 2y = -x - 4
y = -1/2x - 2
Similarly, rearrange equation 2:
2) 8y = -4x - 16
y = -1/2x - 2
When we compare the equations in slope-intercept form, we can see that they have the same slope (-1/2) and the same y-intercept (-2). This means that the two equations represent the same line and have an infinite number of solutions.
Therefore, the linear equations x + 2y = -4 and 4x + 8y = -16 have infinite solutions.
The given equations are:
1) x + 2y = -4
2) 4x + 8y = -16
We can rearrange equation 1 to find the slope-intercept form:
1) 2y = -x - 4
y = -1/2x - 2
Similarly, rearrange equation 2:
2) 8y = -4x - 16
y = -1/2x - 2
When we compare the equations in slope-intercept form, we can see that they have the same slope (-1/2) and the same y-intercept (-2). This means that the two equations represent the same line and have an infinite number of solutions.
Therefore, the linear equations x + 2y = -4 and 4x + 8y = -16 have infinite solutions.