{ 2х+ү=8 {3х +4ү=7

To solve the system of equations:

1. \( 2x + y = 8 \) (Equation 1)
2. \( 3x + 4y = 7 \) (Equation 2)

We can use the substitution or elimination method. Here, I will use the substitution method.

Step 1: Solve for \( y \) in Equation 1

From Equation 1: \[ y = 8 - 2x \]

Step 2: Substitute \( y \) into Equation 2

Now, substitute \( y \) in Equation 2: \[ 3x + 4(8 - 2x) = 7 \]

Step 3: Distribute and simplify

Now distribute: \[ 3x + 32 - 8x = 7 \] Combine like terms: \[ -5x + 32 = 7 \]

Step 4: Solve for \( x \)

Now, isolate \( x \): \[ -5x = 7 - 32 \] \[ -5x = -25 \] \[ x = 5 \]

Step 5: Substitute \( x \) back to find \( y \)

Now substitute \( x = 5 \) back into the expression for \( y \): \[ y = 8 - 2(5) \] \[ y = 8 - 10 \] \[ y = -2 \]

Solution

The solution to the system of equations is: \[ x = 5 \] \[ y = -2 \]

So, the ordered pair \( (x, y) \) is \( (5, -2) \).