5x+3y=9(I)
2x−3y=12(II)
(linear equations, system of equations, variables, coefficients)
Get the complete, step-by-step math solution for: "5x + 3y = 9 (I) 2x - 3y = 12 (II) (linear equations, system of equations, variables, coefficients)". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Add the two equations
We have a system of two linear equations. Notice that the coefficients of y are +3 and −3. Adding the two equations together will eliminate the y variable, allowing us to solve for x.
Step 2: Simplify and solve for x
After adding the equations, the 3y and −3y terms cancel out, leaving us with 7x=21. Dividing both sides by 7 gives us the value of x.
Step 3: Substitute x into one of the original equations
Now that we have the value of x, we can substitute it into either of the original equations to find the value of y. Let's use Equation (I): 5x+3y=9.
Step 4: Solve for y
Substitute x=3 into the equation 5x+3y=9. This simplifies to 15+3y=9. Subtract 15 from both sides to get 3y=−6, and then divide by 3 to find y=−2.