Solve the following equations `x +4y = 2 and 4x -y = -9` by the graphical method and check the result

Explanation

(a) `x + 4y = 2`
`{:(x,2," 6",-2,-6),(y = (2-x)/(4),0,-1," 1"," 2"):}`
Some of the ordered pairs which satisfy the equation `x + 4y = 2 " are " (2,0), (6, -1), (-2, 1), (-6,2)`
(b) `4x - y = -9`
`{:(x,-1,-2,0),(y = 4x + 9,5,1,9):}`
Some of the ordered pairs which satisfy the equation `4x - y = -9 " are " (-1,5), (-2,1),(0,9)`. By plotting the above points on graph sheet, we get the following graph.

From the graph, it is clear that, the given equations intersect at `(-2,1)`. Therefore, it is the common solution for the equatijon `x + 4y = 2 and 4x - y = -9`
Verification
`x + 4y =2` (1)
`4x -y = -9` (2)
By solving Eqs. (1) and (2), we get `x = -2 and y =1`
`:.` The solution is `(-2, 1)`
Hence, verified