Question

X y = 2. 2x 7y = 9. Solve each system by the elimination method

Answer 1

The system of equations x + y = 2 and 2x + 7y = 9 was solved using the elimination method, and the solution found was x = 1 and y = 1.

Step-by-step explanation:

To solve the system of equations x + y = 2 and 2x + 7y = 9 using the elimination method, we need to eliminate one variable by making the coefficients of either x or y the same in both equations. Let's aim to eliminate x by manipulating the equations.

First, we need to multiply the first equation by -2 so that when we add it to the second equation, x will be eliminated:

• -2(x + y) = -2(2)
• -2x - 2y = -4

Now, add this new equation to the second equation:

• (-2x - 2y) + (2x + 7y) = -4 + 9
• -2x + 2x - 2y + 7y = 5
• 5y = 5

Divide both sides by 5 to find y:

• y = 5/5
• y = 1

Now that we have the value of y, substitute it back into the first equation to find x:

• x + 1 = 2
• x = 2 - 1
• x = 1

Thus, the solution to the system is x = 1 and y = 1.