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Question: Identify the graph that represents the system of linear equations.
2x + 5y = 12
x + y = 3



A ) Graph 4
B ) Graph 2
C ) Graph 3
D ) Graph 1

Steps to derive

1 The given two equations are 2x + 5y = 12 and x + y = 3.

1 The given two equations are 2x + 5y = 12 and x + y = 3.

2 Write each equation in slope-intercept form.
2x + 5y = 12
5y = -2x + 12
y = -25 x + 125
x + y = 3
y = -x + 3


2 Write each equation in slope-intercept form.
2x + 5y = 12
5y = -2x + 12
y = -25 x + 125
x + y = 3
y = -x + 3


3 Graph both equations.


3 Graph both equations.


4 From the graph, the point of intersection is (1, 2).

4 From the graph, the point of intersection is (1, 2).

5 To check whether (1, 2) is a solution, substitute 1 for x and 2 for y in each of the original equations.
2x + 5y = 12 2(1) + 5(2) = 12 12 = 12
x + y = 3 (1) + (2) = 3 3 = 3

5 To check whether (1, 2) is a solution, substitute 1 for x and 2 for y in each of the original equations.
2x + 5y = 12 2(1) + 5(2) = 12 12 = 12
x + y = 3 (1) + (2) = 3 3 = 3

6 Among the graphs, the Graph 2 shows the intersecting point of the lines of two given equations 2x + 5y = 12 and x + y = 3.

6 Among the graphs, the Graph 2 shows the intersecting point of the lines of two given equations 2x + 5y = 12 and x + y = 3.

7 So, Graph 1 represents the exact graphs of the given system of linear equations.

7 So, Graph 1 represents the exact graphs of the given system of linear equations.



Hence the right answer is Option B

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