Identify the solution (x,y) of the system of linear equations: Line 1 (red): y=2x+1 Line 2 (blue): y−5=− 1 2x+3
To find the solution of the system of linear equations, we need to solve the equations simultaneously.
Equation 1: y = 2x + 1
Equation 2: y - 5 = - 1/2 * x + 3
We can solve Equation 2 for y:
y = (-1/2)x + 8
Now we can substitute this value of y into Equation 1:
2x + 1 = (-1/2)x + 8
Multiplying both sides of Equation 1 by 2 to eliminate the fractions:
4x + 2 = -x + 16
Combining like terms:
5x + 2 = 16
5x = 14
x = 14/5
Substituting the value of x back into Equation 1 to find y:
y = 2(14/5) + 1
y = 28/5 + 1
y = 28/5 + 5/5
y = 33/5
Therefore, the solution to the system of equations is (x, y) = (14/5, 33/5).