Question

Determine the number and types of solutions for the system:3x+2y=4y=-3/2x+6

Answer 1

No Solution

Step-by-step explanation:

Given the system of linear equations:

`\begin{gathered} 3x+2y=4\ldots(1) \\ y=-(3)/(2)x+6​\ldots(2) \end{gathered}`

If we make y the subject of the equation in Equation 1, we have:

`\begin{gathered} 2y=-3x+4 \\ y=-(3)/(2)x+(4)/(2) \\ y=-(3)/(2)x+2 \end{gathered}`

The two equations are in the slope-intercept form: y=mx+b

We see that the coefficient of x in both equations is -3/2.

Therefore, the slopes of both lines = -3/2

Since the slopes are the same, the two lines are parallel.

Therefore, the system of equations has No Solution.