Question

On your own paper, graph the system of equations and identify the solution.=2−4=−12+1

Answer 1

The Slope-Intercept Form of the equation of a line is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

You have the first line:

`=2x-4`

You can identify that the y-intercept is:

`b_1=-4`

You can find the x-intercept substituting the following value of "y" into the equation of the line:

`y=0`

And, after the substitution, you can solve for "x":

`\begin{gathered} 0=2-4 \\ 4=2x \\ \\ (4)/(2)=x \\ \\ x=2 \end{gathered}`

Now you know that the first line passes through these points:

`\begin{gathered} (0,-4) \\ (2,0) \end{gathered}`

Then, you can graph it.

Given the second line:

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

You can identify that:

`b_2=1`

And you can find the x-intercept by following the same procedure applied for the first line:

`\begin{gathered} 0=-(1)/(2)x+1 \\ \\ -1=-(1)/(2)x \\ \\ (-1)(2)=-x \\ \\ -2=-x \\ x=2 \end{gathered}`

Then, this line passes through these points:

`\begin{gathered} (0,1) \\ (2,0) \end{gathered}`

Now you can graph it.

See the graph below:

By definition, when the lines intersect, the solution of the System of equations is the point where the two lines intersect.

The answer is: First option.