Solve the system by substitution: y=−2x+1 −9x−2y=3
To solve the system by substitution, we need to substitute the value of y in the second equation with its equivalent value from the first equation.
First, we rewrite the first equation to solve for x:
y = -2x + 1
Rearranging the equation, we get:
2x = -y + 1
x = (-1/2)y + 1/2
Now, substitute this expression for x in the second equation:
-9x - 2y = 3
-9((-1/2)y + 1/2) - 2y = 3
(9/2)y - 9/2 - 2y = 3
(9/2 - 4/2)y - 9/2 = 3
((9 - 4)/2)y - 9/2 = 3
(5/2)y - 9/2 = 3
5y - 9 = 6
5y = 6 + 9
5y = 15
y = 15/5
y = 3
Now that we have the value of y, we can substitute it back into the first equation to find x:
y = -2x + 1
3 = -2x + 1
2x = 1 - 3
2x = -2
x = -2/2
x = -1
Therefore, the solution to the system of equations is x = -1 and y = 3.