Solve each system
3x+2y= -2
9x- y= -6
I know how to solve for x
but i get really lost trying to figure out how to solve for the second variable
well, if you have solved for x, then put that value of x into EITHER equation, and solve for y.
To solve the given system of equations:
3x + 2y = -2
9x - y = -6
We can solve for the second variable, y, by using the method of substitution. Here's the step-by-step process:
1. Solve one of the equations for one variable in terms of the other variable. Let's solve the second equation, 9x - y = -6, for y:
y = 9x + 6
2. Substitute this expression for y in the other equation. Replace y in the first equation, 3x + 2y = -2, with 9x + 6:
3x + 2(9x + 6) = -2
3. Simplify and solve the resulting equation for x:
3x + 18x + 12 = -2
21x + 12 = -2
21x = -2 - 12
21x = -14
x = -14/21
x = -2/3
4. Substitute this value of x back into one of the original equations to solve for y. Let's use the second equation, 9x - y = -6:
9(-2/3) - y = -6
-6 - y = -6
-y = -6 + 6
-y = 0
y = 0
5. The solution to the system of equations is x = -2/3 and y = 0.
Therefore, the solution to the given system is x = -2/3 and y = 0.