Question

The system of linear equations is given as
$y+2x=4$
$2y+4y=6$
Which of the following is the solution to the above system?

• A. $(2,1)$
• B. $(1,1)$
• C. $(-1,1)$
• D. $\text{No solution}$

Answer 1

The correct option is D $\text{No solution}$

Given equations are:
$y+2x=4$
$2y+4y=6$
Step 1: Simplify the equation if possible,

Equation (1) $\to$ $y+2x=4$ cannot be simplified further

$2y+4y=6$ can be simplified
So, on dividing both sides by 2, we get
Equation (2) $\to$ y + 2y = 3

Step 2:
Write the above equations in slope- intecept form $y=mx+b$

Equation (1)
$y+2x=4\to y=-2x+4$

Equation (2)
$2y+4y=6\to y=-2x+3$

Step 3:
Compare the above two equations with the slope - intercept form (y=mx+b)
Slope, m=-2 is same for both lines
Intercepts,
$y=-2x+4\to$ b =4
$y=-2x+3\to$ b = 3

$\therefore$ The two equations of the system have the same slope, but the intercepts are different.

Concept: The two lines are parallel if the slopes are the same, but the intercepts are different. When the two different equations represent two different parallel lines, then the pair of equations has no solution.

$\therefore$ Answer: No solution