To solve the system of equations:
- \( 5x - y = 21 \) (Equation 1)
- \( x = 2y - 3 \) (Equation 2)
We can substitute Equation 2 into Equation 1.
From Equation 2, we have: \[ x = 2y - 3 \]
Now, substitute \( x \) in Equation 1: \[ 5(2y - 3) - y = 21 \]
Expanding this gives: \[ 10y - 15 - y = 21 \]
Combine like terms: \[ 9y - 15 = 21 \]
Now, add 15 to both sides: \[ 9y = 36 \]
Next, divide both sides by 9: \[ y = 4 \]
Now that we have \( y \), we can find \( x \) using Equation 2: \[ x = 2(4) - 3 \] \[ x = 8 - 3 \] \[ x = 5 \]
So the solution to the system of equations is: \[ x = 5, \quad y = 4 \]
We can write the solution as a point: \[ (5, 4) \]
To verify, we can plug \( x \) and \( y \) back into both original equations:
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For \( 5x - y = 21 \): \[ 5(5) - 4 = 25 - 4 = 21 \quad \text{(True)} \]
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For \( x = 2y - 3 \): \[ 5 = 2(4) - 3 = 8 - 3 = 5 \quad \text{(True)} \]
Since both equations are satisfied, the solution is confirmed: \[ \boxed{(5, 4)} \]