Question

Choose the correct solution(s) of the given simulteneous linear equations.
$5x+2y=10y=-\frac{5}{2}x+5$

• A. $(0,5)$
• B. $(1,2.5)$
• C. $(4,-6)$
• D. They have infinitely many solutions.

Answer 1

Answer: (A), (B), (D)

They have infinitely many solutions.

Equation 1:
Let's rewrite the equation $5x+2y=10$ in intercept form.

$5x+2y=10$
Dividing by $10$ in both side.
$\Rightarrow \frac{5x}{10}+\frac{2y}{10}=1$
$\Rightarrow \frac{x}{2}+\frac{y}{5}=1$
$x-$intercept is $2,$ and $y-$intercept is $5.$

Equation 2:
$y=-\frac{5}{2}x+5$ is in slope-intercept form, where slope is $-\frac{5}{2}$ and the $y-$intercept is $5.$

$\therefore \frac{\text{Rate of change of y}}{\text{Rate of change of x}}=\frac{-5}{2}$


Let's plot both the lines in the coordinate plane.

The lines coincide with each other.
$\therefore$ These are the equations of same straight line.
These equations have infinitely many solutions.

The ordered pairs $(0,5)$ and $(1,2.5)$ satisfy the given equation.
However, $(4,-6)$ does not satisfy the given equation.