Solve the simultaneous equations 3x + 2y = 4, 4x + 5y = 17

To solve this pair of simultaneous equation I will use the substitution method however the elimination method could also be used here.
Eq1. 3x + 2y = 4
Eq2. 4x + 5y = 17
First rearrange Eq1. to find y on its own
2y = 4 - 3x
y = 2 - 3x/2
Now substitute this equation into Eq2.
4x + 5(2 - 3x/2) = 17
4x + 10 - 15x/2 = 17
4x - 15x/2 = 7
-7x/2 = 7
-x/2 = 1
x = -2
Now substitute this value for x into the rearranged form of Eq1.
y = 2 - 3(-2)/2
y = 2 +3
y = 5
Solutions: x = -2, y = 5
The solutions to this pair of simultaneous equations can be checked by plugging them back into Eq2.
4(-2) + 5(5) = 17
-8 + 25 = 17
17 = 17 So the solutions to these equations are correct.