Question

The number of solutions of the simultaneous algebraic equations y = 3x + 3 and y = 3x + 5 is
1. Zero
2. 1
3. 2
4. Infinite

Answer 1

Correct Answer - Option 1 : Zero

Concept:

System of equations

a1x + b1y = c1

a2x + b2y = c2

For unique solution

\(\frac {a_1}{a_2}≠ \frac {b_1}{b_2}\)

For Infinite solution

\(\frac {a_1}{a_2}= \frac {b_1}{b_2}= \frac {c_1}{c_2}\)

For no solution

\(\frac {a_1}{a_2}=\frac {b_1}{b_2}≠ \frac {c_1}{c_2}\)

Calculation:

Given:

3x - y= -3

3x - y = -5

a₁ = 3, b₁ = -1 and c₁ = -3

and a₂ = 3, b₁ = -1 and c₂ = -5

\(\frac 3{3}=\frac {-1}{-1}≠ \frac {-3}{-5}\)

Hence this shows that the number of solutions for given simultaneous algebraic equations is zero.