I need help solving systems using elimination 3 * -3y equals - 3 2x minus y equals -5 how do I do this do not know algebra
You have two equations here.
3 * -3y = -3
-9y = -3
Divide both sides by -9.
y = -3/-9 = 1/3
2x - y = -5
Substitute 1/3 for y and solve for x.
To solve a system of equations using elimination, you need to eliminate one variable by adding or subtracting the equations. Here's how you can solve the given system of equations step-by-step:
1. Start with the two equations:
3 * -3y = -3 (Equation 1)
2x - y = -5 (Equation 2)
2. Simplify Equation 1:
By multiplying 3 and -3y, you get: -9y = -3.
3. Simplify Equation 2:
No further simplification is needed for Equation 2 (2x - y = -5).
4. Now, let's eliminate the variable 'y' from the equations.
Since both equations have "-y," we can multiply Equation 2 by -1 to make the coefficients of 'y' same but with opposite signs:
-1 * (2x - y) = -1 * (-5)
Simplifying this, we get: -2x + y = 5 (Equation 3)
5. Now, add Equation 3 to Equation 1:
(-9y) + (y) = (-3) + (5)
Simplifying further, we get: -8y = 2
6. Solve for 'y':
Divide both sides of the equation by -8: y = 2 / -8
This simplifies to: y = -1/4
7. Substitute the value of 'y' back into one of the original equations to solve for 'x'. Let's use Equation 2:
2x - (-1/4) = -5
Simplify this equation: 2x + 1/4 = -5
8. Subtract 1/4 from both sides of the equation:
2x = -5 - 1/4
Simplifying further, we get: 2x = -20/4 - 1/4
9. Combine the fractions on the right side of the equation:
2x = -21/4
10. Divide both sides of the equation by 2 to solve for 'x':
x = (-21/4) / 2
This simplifies to: x = -21/8
So, the solution to the given system of equations is x = -21/8 and y = -1/4.