Question

show graphically that the system of equations x+2y=4 & 7x+4y-18 is consistent with a unique solution

Answer 1

Each of these equations represents a straight line. You find at least two values of x and y for each of these equations which satisfy the equation. Find integral values for x & y so that it is to easy to draw graph.
For example, For x + 2y = 4, when x = 2, y = 1 and when x = 4, y = 0.
These two sets (2,1) and (4,0) represent two points through which the line represented by x + 2y = 4.
Hence on graph draw a line through the points (2,1) and (4,0)

Similarly, points (2,1) and (6, -6) represent two points through which the line represented by 7x + 4y = 18 passes. Draw a line through these points.
You will see that the lines cut each other at only one point.
Hence this presents uniqueness of the solution.

J

Answer 2

$x+2y=4\\\\x-intercept\ (y=0)\\x+2(0)=4\\x=4\to(4;\ 0)\\\\y-intercept\ (x=0)\\0+2y=4\\2y=4\\y=2\to(0;\ 2)\\-----------------------------$

$7x+4y=18\\\\4y=-7x+18\ \ \ \ /:4\\\\y=-\frac{7}{4}x+\frac{18}{4}\\\\for\ x=2\to y=-\frac{7}{4}(2)+\frac{18}{4}=-\frac{14}{4}+\frac{18}{4}=\frac{4}{4}=1\to(2;\ 1)\\\\for\ x=-2\to y=-\frac{7}{4}(-2)+\frac{18}{4}=\frac{14}{4}+\frac{18}{4}=\frac{32}{4}=8\to(-2;\ 8)$


$Solution:x=2\ and\ y=1.$