Question

41. What is the solution to the system?

Answer 1

Both equations represent the same line, so **infinitely many solutions** exist, expressed by the single equation: **y = -2x + 3**.

Let's solve the system of equations:

y=-2x+3

x=
`-(y)/(2)+(3)/(2)`

We can solve the system of equations by elimination.

Steps to solve:

Rearrange terms in standard form:

y+2x=3

`(1)/(2)y+x=(3)/(2)`

Eliminate y:

Multiply the top equation by
`$-1/2$` and add it to the bottom equation:

`$$0=0$$`

Conclusion:

Since the result is 0=0, the lines coincide and represent the same line. Therefore, there are infinitely many solutions.

`$$y=-2x+3$$`