Question

How many solutions do these equations have

Answer 1

`\large\boxed{\bold{one\ solution}\ (1,\ -4)\to x=1,\ y=-4}`

Explanation:

`\left\{\begin{array}{ccc}y=2x-6\\y=-x-3\end{array}\right\\\\\text{These are linear functions. We only need two points to draw a graph.}\\\\\text{Choice two values of x, substitute to the equation,}\\\text{and calculate the values of y.}\\\\y=2x-6\\for\ x=0\to y=2(0)-6=0-6=-6\to(0,\ -6)\\for\ x=3\to y=2(3)-6=6-6=0\to(3,\ 0)\\\\y=-x-3\\for\ x=0\to y=-0-3=0-3=-3\to(0,\ -3)\\for\ x=-3\to y=-(-3)-3=3-3=0\to(-3,\ 0)\\\\\text{Look at the picture}`

`\text{The intersection of the line is the solution of the system of equations:}\\\\(1,\ -4)\to x=1,\ y=-4`