use the substition method to solve the system of equations
5x+2y=1
y=-x+2
To solve the system of equations using the substitution method, we'll begin with the second equation:
y = -x + 2
Now substitute this value of y into the first equation:
5x + 2(-x+2) = 1
Simplify the equation:
5x - 2x + 4 = 1
3x + 4 = 1
Subtract 4 from both sides:
3x = -3
Divide both sides by 3:
x = -1
Now substitute this value of x back into the second equation to solve for y:
y = -(-1) + 2
y = 1 + 2
y = 3
Therefore, the solution to the system of equations is x = -1 and y = 3.