10th Class Mathematics Unit 2 Quadratic Equations Numericals with Solutions

2.2.1.(i) Find the points of intersection of x + y = 8 with the coordinate axes graphically. (ii) Find the points of intersection of x - y = 1 with the coordinate axes graphically. (iii) Find the points of intersection of x - 2y = 1 with the coordinate axes graphically. (iv) Find the points of intersection of x - 2y + 2 = 0 with the coordinate axes graphically. (v) Find the points of intersection of 5x - 5y = 1 with the coordinate axes graphically.

Given

(i) x+y=8

(i) x-intercept (y=0) x=8 ⇒ (8,0)

(i) y-intercept (x=0) y=8 ⇒ (0,8)

Result

(i) (8,0) and (0,8)

Given

(ii) x-y=1

(ii) x-intercept x=1 ⇒ (1,0)

(ii) y-intercept y=-1 ⇒ (0,-1)

Result

(ii) (1,0) and (0,-1)

Given

(iii) x-2y=1

(iii) x-intercept x=1 ⇒ (1,0)

(iii) y-intercept y=-frac12 ⇒ left(0,-frac12right)

Result

(iii) (1,0) and left(0,-frac12right)

Given

(iv) x-2y+2=0

(iv) x-intercept x=-2 ⇒ (-2,0)

(iv) y-intercept y=1 ⇒ (0,1)

Result

(iv) (-2,0) and (0,1)

Given

(v) 5x-5y=1

(v) x-intercept x=frac15 ⇒ left(frac15,0right)

(v) y-intercept y=-frac15 ⇒ left(0,-frac15right)

Result

(v) left(frac15,0right) and left(0,-frac15right)

2.2.2.(i) Solve the system of linear equations graphically: x + y = 8, 3x - y = 4. (ii) Solve the system of linear equations graphically: x - y = 1, x + 2y = 7. (iii) Solve the system of linear equations graphically: x - 2y = 1, 2x + y = 2. (iv) Solve the system of linear equations graphically: y = 2x + 2, 3x + 2y = 4. (v) Solve the system of linear equations graphically: 3y = 2x + 8, x + y = 1.

2.2.3.(i) Solve graphically: y = 8x - 32 and y = x² - 6x + 8. (ii) Solve graphically: y + x = 2 and y = 2x² + x - 10.

Unit 2: Quadratic Equations — Exercise 2 2