Question
Solve the following sets of simultaneous equations : x + y = 4 ; 2x – 5y = 1
✓
Answer
Substitution Method:
x + y = 4
∴ x = 4 – y …(i)
2x – 5y = 1 ……(ii)
Substituting x = 4 – y in equation (ii),
2(4 – y) – 5y = 1
∴ 8 – 2y – 5y = 1
∴ 8 – 7y = 1
∴ 8 – 1 = 7y
∴ 7 = 7y
$\therefore y=\frac{7}{7}$
x + y = 4
∴ x = 4 – y …(i)
2x – 5y = 1 ……(ii)
Substituting x = 4 – y in equation (ii),
2(4 – y) – 5y = 1
∴ 8 – 2y – 5y = 1
∴ 8 – 7y = 1
∴ 8 – 1 = 7y
∴ 7 = 7y
$\therefore y=\frac{7}{7}$
Substituting y = 1 in equation (i),
x = 4 – 1 = 3
∴ (3,1) is the solution of the given equations.
Alternate method:
Elimination Method:
x + y = 4 …(i)
2x – 5y = 1 ……(ii)
Multiplying equation (i) by 5,
5x + 5y = 20 … (iii)
Adding equations (ii) and (iii),
2x – 5y = 1
+ 5x + 5y = 20
7 = 21
$\therefore x=\frac{21}{7}$
∴ x = 3
Substituting x = 3 in equation (i),
3 + y = 4
∴ y = 4 – 3 = 1
(3,1) is the solution of the given equations.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A field is $200m$ long and $150m$ broad. There is a plot, $50m$ long and $40m$ broad, near the field. The plot is dug $7m$ deep and the earth taken out is spread evenly on the field. By how many meters is the level of the field raised? Give the answer to the second place of decimal.
→By equating coefficients of variables, solve the following equations : x – 2y = -10 ; 3x – 3y = -12
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
Solve the following sets of simultaneous equations : 3x – 5y = 16; x – 3y= 8
Find the following products:
$(4 x-3 y+2 z)\left(16 x^2+9 y^2+4 z^2+12 x y+6 y z-8 z x\right)$
→$(4 x-3 y+2 z)\left(16 x^2+9 y^2+4 z^2+12 x y+6 y z-8 z x\right)$
Give two rational numbers lying between 0.232332333233332 and 0.212112111211112.
The dimensions of a cinema hall are $100m, 50m, 18m.$ How many persons can sit in the hall, if each person requires $150m^3$ of air?
→In figure, lines AB and CD intersect at O. If $\angle\text{AOC}+\angle\text{BOE}=70^\circ$ and $\angle\text{BOD}=40^\circ,$ find $\angle\text{BOE}$ and reflex $\angle\text{COE}.$
→The external dimensions of a closed wooden box are $48cm, 36cm, 30cm$. The box is made of 1.5cm thick wood. How many bricks of size $6cm \times 3cm \times 0.75cm$ can be put in this box?
→In the adjoining figure, DE || BC. Prove that:
→- $\text{ar}(\triangle\text{ACD})=\text{ar}(\triangle\text{ABE})$
- $\text{ar}(\triangle\text{OCE})=\text{ar}(\triangle\text{OBD}).$