Question

-4x+7y=21
4x-9y=-27

Solve this problem using elimination.

Answer 1

The solution to the system of equations -4x + 7y = 21 and 4x - 9y = -27 using elimination is x = 0 and y = 3. By adding both equations, the x terms are eliminated, leading to solving for y, then x. The solution is checked and is reasonable.

Step-by-step explanation:

Solving Simultaneous Equations Using Elimination

To solve the system of equations using elimination, we need to manipulate the equations in a way that allows us to eliminate one of the variables. The given equations are:

• -4x + 7y = 21
• 4x - 9y = -27

To eliminate the x-term, we can add both equations together. When we add them, the x terms cancel out:

• (-4x + 7y) + (4x - 9y) = 21 - 27
• 0x - 2y = -6

Now, we can solve for y:

• -2y = -6
• y = 3

Next, we will substitute y = 3 into one of the original equations to find the value of x. We'll use the first equation -4x + 7y = 21.

• -4x + 7(3) = 21
• -4x + 21 = 21
• -4x = 0
• x = 0

So, the solution to the system of equations is x = 0 and y = 3.

We check the answer by plugging x and y back into both original equations to ensure they are true:

• -4(0) + 7(3) = 21, which simplifies to 0 + 21 = 21
• 4(0) - 9(3) = -27, which simplifies to 0 - 27 = -27

Both equations check out, so the solution is reasonable.