# Graphical Method of Finding Solution of a Pair of Linear Equations

## Trending Questions

**Q.**

Draw the graphs of the equations $x-y+1=0$ and $3x+2y-12=0$. Determine the coordinates of the vertices of the triangle formed by these lines and the $x$-axis and shade the triangular region.

**Q.**

Question 1 (i)

Form the pair of linear equations in the following problems, and find their solutions graphically.

10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

**Q.**Solve the following systems of equations:

3x − 7y + 10 = 0

y − 2x − 3 = 0

**Q.**

Draw the graphs of the equations $x=3,x=5$ and $2x-y-4=0$. Also find the area of the quadrilateral formed by the lines and the $x$-axis.

**Q.**Question 10

Find the solution of the pair of equations x10+y5−1=0 and x8+y6=15 find λ, if y=λx+5

**Q.**Draw the graph of the following pair of linear equations :

x+3y=6 and 2x−3y=2

Find the ratio of the areas of the two triangles formed by first line, x=0, y=0 and second line, x=0, y=0.

**Q.**Question 4

The cost of 4 pens and 4 pencils boxes is Rs.100. there times the cost of a pen is Rs. 15 more than the cost of a pencil box, . Form the pair of linear equations for the above situation. Find the cost pen and a pencil box be Rs. y.

**Q.**

If the cost of $2$ pencils and $3$ erasers is $Rs.9$ and the cost of $4$ pencils and $6$ erasers is $Rs.18$ . Find the cost of each pencil and each eraser.

**Q.**

If the length and breadth of the room are increased by 1 m each, its area would be increased by $31{\text{m}}^{2}$. If the length is increased by 1 m and breadth is decreased by 1 m, the area would decrease by $9{\text{m}}^{2}$ . Find the area of the floor of the room in ${\text{m}}^{2}$.

$200$

$209$

$250$

$150$

**Q.**At what point will the line x-y = 8 intersect y axis?

**Q.**

Find the value of ‘a" for which the system of equations 3x + 2y - 4 = 0 and ax - y - 3 = 0, will represent intersecting lines.

a = 3/2

a = 2/3

a ≠ -3/2

a ≠ -2/3

**Q.**

The coordinates of the point in which the line joining the points $(3,5,-7)$ and $(-2,1,8)$is intersected by the plane $yz$ are given by

$\left(0,\frac{13}{5},2\right)$

$\left(0,\frac{-13}{5},-2\right)$

$\left(0,\frac{-13}{5},\frac{2}{5}\right)$

$\left(0,\frac{13}{5},\frac{2}{5}\right)$

**Q.**Question 4 (i)

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs 1180 as hostel charges. Find the fixed charges and the cost of food per day.

**Q.**Question 4

The pair of equation y = 0 and y = - 7 has

(A) one solution

(B) two solutions

(C) infinitely many solutions

(D) no solution

**Q.**

The graphs of the equations 2x+3y-2=0 and x-2y-8=0 are two lines which are

(a) coincident

(b) parallel

(c) intersecting exactly at one point

(d) perpendicular to each other

**Q.**Show graphically that each one of the following systems of equations has infinitely many solutions:

x − 2y + 11 = 0

3x − 6y + 33 = 0

**Q.**What is the solution for the two lines given in the graph?

- x=0, y=0
- x=4, y=2
- x=5, y=2
- x=−5, y=2

**Q.**Solve the following systems of equations:

$\frac{2}{x}+\frac{5}{y}=1\phantom{\rule{0ex}{0ex}}\frac{60}{x}+\frac{40}{y}=19,x\ne 0,y\ne 0$

**Q.**

Solve each of the following systems of equations graphically:

3x+2y=4, 2x−3y=7.

**Q.**

Show graphically that each of the following given systems of equations is inconsistent.i.e., has no solution:

2x+3y=4, 4x+6y=12.

**Q.**

Solve each of the following systems of equations graphically:

2x−3y+13=0, 3x−2y+12=0.

**Q.**Draw the graph of y=2x2 and hence solve 2x2+x−6=0 .

- {2, 1.5}
- {-2, 1.5}
- {-2, -1.5}
- {2, -1.5}

**Q.**If 5+2√37+4√3=a+b√3 , then find the value of a and b

**Q.**

Find the values of a and b for which the following system of equations has infinitely many solutions:

(i) (2a - 1) x - 3y = 5

3x + (b - 2) y = 3

(ii) 2x - (2a + 5) y = 5

(2b + 1) x - 9y = 15

(iii) (a - 1) x + 3y = 2

6x + (1 - 2b) y = 6

(iv) 3x + 4y = 12

(a + b) x + 2 (a - b) y = 5a - 1

(v) 2x + 3y = 7

(a - b) x + (a + b) y = 3a + b - 2

(vi) 2x + 3y - 7 = 0

(a - 1) x + (a + 1) y = (3a - 1)

(vii) 2x + 3y = 7

(a - 1) x + (a + 2) y = 3a

(viii) x + 2y = 1

(a - b) x + (a + b) y = a + b - 2

(ix) 2x + 3y = 7

2ax + ay = 28 - by

**Q.**Solve the following pair of equations by reducing them to a pair of linear equations:

1x−4y=21x−3y=9

**Q.**

Question 7

How many solution(s) of the equation 2x + 1 = x - 3 are there on the:

(i) number line?

(ii) Cartesian plane?

**Q.**Solve the following systems of equations:

152x − 378y = −74

−378x + 152y = −604

**Q.**

The number of solutions of equations represented by this graph is

No Solution

Infinite

2

1

**Q.**Question 7

Draw the graphs of the equations x - y + 1 = 0 and 3x + 2y - 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

**Q.**Question 3

The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically