Question

Considering the following system of equations x+y=5 2x-y=-2 and determine the solution to the system of equations

Answer 1

Given the System of Equations:

`\begin{cases}x+y=5 \\ 2x-y={-2}\end{cases}`

Part A

You can sketch the graph of the System of Linear Equations as follows:

1. Find the x-intercept of the first line by substituting this value of "y" into the first equation and solving for "x" (because the y-value is zero when the line intersects the x-axis):

`y=0`

Then, you get:

`\begin{gathered} x+0=5 \\ x=5 \end{gathered}`

2. Find the y-intercept of the first line by substituting this value of "x" into the first equation and solving for "y" (because the x-value is zero when the line intersects the y-axis):

`x=0`

Then:

`\begin{gathered} 0+y=5 \\ y=5 \end{gathered}`

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

`(5,0),(0,5)`

3. Find the x-intercept of the second line applying the same procedure used with the first line:

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

4. Find the y-intercept of the second line applying the same procedure used with the first line:

`\begin{gathered} 2(0)-y=-2 \\ -y=-2 \\ y=2 \end{gathered}`

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

`(-1,0),(0,2)`

5. Graph both lines in the same Coordinate Plane:

Part B

By definition, when two lines of a System of Equations intersect each other, the system has one solution. The solution is the point of intersection between the lines. In this case, it is:

Hence, the answers are:

Part A

Part B

`(1,4)`