Question

find the solution set of the following equation graphically (find four ordered pairs)
x-2y=-3,
2x+y=14

Answer 1

Answer:

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Step-by-step explanation:

For x+2y=-3,

The ordered pairs are (1,-2),(-1,-1),(-3,0),(3,-3).

For 2x+y=14

The ordered pairs are (7,0),(6,2),(5,4),(4,6).

Answer 2

Answer: (1,2),(3,3),(5,4),(7,5) are the ordered pairs of the equation x-2y=-3.

(0,14),(1,12),(2,10),(3,8) are the ordered pairs of the equation, 2x+y=14.

Step-by-step explanation:

Consider the given equations,

x-2y=-3- - - - - - - > (1)

2x+y=14 - - - - - -  >(2)

Consider equation (1) and solve for y,

                $x-2y=-3\\x+3=2y\\\\y=\frac{x+3}{2}$- - - - - >(3)

• put x=1 in the above equation

                $y = \frac{1+3}{2} \\\\y= \frac{4}{2} \\\\y=2$

• put x=3 in (3),

               $y=\frac{3+3}{2} \\\\y=3$

• put x=5 in (3)

(The reason for choosing x as only odd numbers is because an addition of two numbers gives an even number and, since we have two in the denominator, we get a whole number as the answer.)

             

                 $y=\frac{5+3}{2} \\\\y=4$

• put x=7 in (3)

                $y=\frac{7+3}{2}\\ \\y=5$

∴ (1,2),(3,3),(5,4),(7,5) are the ordered pairs of the equation x-2y=-3.

Consider (2),

That is, 2x+y=14 and solve it for y,

                  $y=14-2x$ - - - - - (4)

• put x=0 in the above equation,

                  $y = 14$

• put x=1 in (4)

                  $y=14-2*1\\y=12$

• put x=2 on (4)

                  $y = 14 - 2*2\\y=10$

• put x=3 on (4)

                  $y=14-2*3\\y=14-6\\y=8$

∴ (0,14),(1,12),(2,10),(3,8) are the ordered pairs of the equation, 2x+y=14.

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