I will solve this equation simultaneously by Substitution.
- x + y = 2
5x + 4y = 17
Solve - x + y = 2 for y:
- x + y + x = 2 + x (here we add x to both sides)
y = x + 2
Substitute x + 2 for y in 5x + 4y = 17
5x + 4y = 17
5x + 4(x + 2) = 17
5x + 4x + 8 = 17
9x + 8 = 17 (simplify both sides of the equation)
9x + 8 + (-8) = 17 + (-8) (add -8 to both sides)
9x = 9
9x/9 = 9/9 (divide both sides by 9)
x = 1
Substitute 1 for x in y = x + 2
y = x + 2
y = 1 + 2
y = 3 ( simplify both sides of the equation)
Therefore x = 1 and y = 3