Question

Solve the following pair of linear equations graphically. Also write the observations.

(i) x + y = 1 ; 2x - 3y = 7

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Answer 1

Step-by-step explanation:

Given:

$x + y =1 \\2x - 3y = 7$

To find: Solution of linear pair of equation graphically.

Solution:

Step 1: Find points to plot x+y=1

Put x=0

0+y=1

y=1

let it is A(0,1)

Put y=0

x+0=1

x=1

let it is B(1,0)

Plot points on graph,make a straight line by joining these points.

Step 2: Find points to plot 2x-3y=7

Put x=0

0-3y=7

y= -2.3

let it is C(0,-2.3)

Put y=0

2x+0=7

x=3.5

let it is D(3.5,0)

Plot points on graph,make a straight line by joining these points.

Graph is attatched.

The line intersects each other at (2,-1),this is the unique solution of these lines.

Final answer:

(2,-1) is the solution of given equations.

Hope it helps you.

To learn more on brainly:

solve the following system of linear equation graphically: 3x+y-11=0 and x-y-1=0

shade the region bounded by these lines...

https://brainly.in/question/3050092

Answer 2

Question 1 :-

(i) x + y = 1 ; 2x - 3y = 7

First equation :- x + y = 1

Case 1 :- Let us consider that x equals 0.

→ x + y = 1

→ 0 + y = 1

→ y = 1

∴ First pair → (0, 1)

Case 2 :- Let us consider that x equals 1.

→ x + y = 1

→ 1 + y = 1

→ y = 1 - 1

→ y = 0

∴ Second pair → (1, 0)

Case 3 :- Let us consider that x equals -1.

→ x + y = 1

→ -1 + y = 1

→ y = 1 + 1

→ y = 2

∴ Third pair → (-1, 2)

Plot the points (0, 1), (1, 0), (-1, 2) on a graph, and join the points, the resulting line represents x + y = 1. [Blue line]

Second equation :- 2x - 3y = 7

→ 2x - 3y = 7

→ 2x - 7 = 3y

→ (2x - 7)/3 = y [We'll be substituing values in this equation]

Case 1 :- Let us consider that x equals 5.

→ (2x - 7)/3 = y

→ (2(5) - 7)/3 = y

→ (10 - 7)/3 = y

→ 3/3 = y

→ y = 1

∴ First pair → (5, 1)

Case 2 :- Let us consider that x equals -1.

→ (2x - 7)/3 = y

→ (2(-1) -7)/3 = y

→ (-2 -7)/3 = y

→ -9/3 = y

→ y = -3

∴ Second pair → (-1, -3)

Case 3 :- Let us consider that x equals -4.

→ (2x - 7)/3 = y

→ (2(-4) - 7)/3 = y

→ (-8 -7)/3 = y

→ -15/3 = y

→ y = -5

∴ Third pair → (-4,-5)

Plot the points (5, 1), (-1, -3), (-4,-5) on a graph, and join the points, the resulting line represents 2x - 3y = 7. [Red line]

Observations :-

• From the graph, it's apparent that the two lines intersect at the point (2, -1), therefore the solution is (2, -1).

• The pair of lines are intersecting lines, they contain only one solution, and only have one point in common.