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

Considering the following system of equations x+y=5 2x-y=-2 and determine the solution-example-1
User Reunanen
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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)

Considering the following system of equations x+y=5 2x-y=-2 and determine the solution-example-1
Considering the following system of equations x+y=5 2x-y=-2 and determine the solution-example-2
Considering the following system of equations x+y=5 2x-y=-2 and determine the solution-example-3
User AlexanderLedovsky
by
8.6k points

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