Answer: X = 1 and Y = 3
Step-by-step explanation: The question shows a pair of simultaneous equations that can be solved by graphical, substitution or elimination methods. However the instruction is to solve by substitution.
To do this, we make one of the unknown variables the subject of the equation (either equation 1 or 2) and then insert the value into its place in the other equation.
The equations are
Y = 2X + 1 —————(1)
Y = -X + 4 —————(2)
Since the Y variable is already the subject of the equation in either of the two equations, we can choose any of the two.
So, we shall choose equation 1. If
Y = 2X + 1
Substitute for the value of Y into equation 2. Then we shall have;
Y = -X + 4
Becomes
2X + 1 = -X + 4
By collecting like terms we now have
2X + X = 4 - 1
{Remember that when a positive value crosses to the other side of an equation, it becomes negative, and vice versa}
3X = 3
Divide both sides of the equation by 3
X = 1
Having calculated the value of the X variable, we can now substitute it into either of the equations. Let us take equation 1. When X = 1
Y = 2X + 1 becomes
Y = 2(1) + 1
Y = 2 + 1
Y = 3.
Hence we have X = 1 and Y = 3