Question

Solve the system using Elimination: x + 2y = 7, 3x - 2y = 5.

a) (1, 3)
b) (3, 2)
c) (7, 5)
d) (2, 3)

Answer 1

The solution to the system of equations x + 2y = 7 and 3x - 2y = 5 using elimination is (3, 2), aligning with option b).

Step-by-step explanation:

To solve the system using elimination, we manipulate the given linear equations to eliminate one variable and solve for the other. The provided equations are:

• x + 2y = 7
• 3x - 2y = 5

We can add these two equations together to eliminate 'y'.

(x + 2y) + (3x - 2y) = 7 + 5

The '2y' terms cancel each other out, leaving us with:

4x = 12

Divide by 4 to solve for 'x':

x = 12 / 4

x = 3

To solve for 'y', substitute x = 3 into the first equation:

3 + 2y = 7

Subtract 3 from both sides of the equation:

2y = 7 - 3

2y = 4

Now, divide by 2 to solve for 'y':

y = 4 / 2

y = 2

The solution to the system of equations is (3, 2), which corresponds to option b).