Question

Consider the simultaneous linear equations
$3x+4y=1$
And, $9x+12y=3$.
How many solutions does this system of equations have?

• A. No solution
• B. Infinitely many solution
• C. Unique solution
• D. Two solution

Answer 1

The correct option is B Infinitely many solution

Given, simultaneous equations:
$3x+4y=1$ $......\left(1\right)$
$9x+12y=3$ $......\left(2\right)$
On simplifying equation $\left(2\right)$ by dividing both side by $3$ we get,
$\frac{9x+12y}{3}=\frac{3}{3}$
$\Rightarrow 3x+4y=1$
This is same equation as equation $\left(1\right)$.
So, They both will overlap with each other on coordinate plane. And all the ordered pair of equation $\left(1\right)$ will satisfy equation $\left(2\right)$.
Plotting it on coordinate plane by first converting given equation in slope intercept form $y=mx+c$, we get
$3x+4y=1\Rightarrow 4y=-3x+1$
$\Rightarrow y=-\frac{3}{4}x+\frac{1}{4}$.
Slope $=-\frac{3}{4}$ and y-intercept $=\frac{1}{4}$


$\Rightarrow$ They have infinitely many solutions.