y = 2−x and y = 4x + 3
Let I be the point of intersection:
I belongs to the line y=2-x and at the same time I belongs to y=4x+3, then the coordinates of I are the same for y =2-x & y= 4x+2, in short if we replace the coordinates in y = 2-x & in y=4x+3 by their respective values, we will find an equality.
b) 2−x = 4x + 3
Replace x in the equation 2−x = 4x + 3 with the here below values to find if an equality exists
for x = -3 then 2-(-3) = 4(-3)+3 → 5 = -9 IMPOSSIBE, it's not an equality
for x = 2 then 2-2 = 4(2)+3 → 0 = 11 IMPOSSIBE, it's not an equality
for x = 1 then 2-(1) = 4(1)+3 → 1 = 7 IMPOSSIBE, it's not an equality
for x = - 1 then 2-(-1) = 4(-1)+3 → 3 = -1 IMPOSSIBE, it's not an equality
and you can replace x with all integers from - 3 to + 3 and you will find an INEQUALITY, so all these values are not a solution of thev equation
c. Solving the equation 2−x = 4x + 3
2−x = 4x + 3
1st add x to both sides: 2-x + x = 4x + 3 + x →2 = 5x + 3
2nd to this new equation 2 = 5x + 3, subtract 3 from both sides:
2 - 3= 5x + 3 - 3 →-1 = 5x
3rd in this new equation -1=5x, divide both sides by 5 → -1/5 = x
And x = -1/5 is the solution of the system. To find the y value, you replace in any of the 2 equation y = 2−x and y = 4x + 3, x by its value (-1/5) and you will find y = 11/5
