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Sagot :
Answer:
Step-by-step explanation:
To solve the simultaneous equations using the elimination method, we start with the given equations:
1. \( 5x - y = 18 \)
2. \( x + y = 6 \)
First, we'll eliminate one of the variables by adding or subtracting the equations. Let's eliminate \( y \) by adding the two equations together.
Adding equation (1) and equation (2):
\[ (5x - y) + (x + y) = 18 + 6 \]
Simplify the left side:
\[ 6x = 24 \]
Now, solve for \( x \):
\[ x = \frac{24}{6} \]
\[ x = 4 \]
Now that we have \( x = 4 \), substitute this value back into equation (2) to find \( y \):
\[ 4 + y = 6 \]
Subtract 4 from both sides:
\[ y = 6 - 4 \]
\[ y = 2 \]
So, the solutions to the simultaneous equations are \( x = 4 \) and \( y = 2 \).
To verify:
Substitute \( x = 4 \) and \( y = 2 \) back into equation (1):
\[ 5(4) - 2 = 20 - 2 = 18 \]
Equation (1) holds true.
Substitute \( x = 4 \) and \( y = 2 \) back into equation (2):
\[ 4 + 2 = 6 \]
Equation (2) also holds true.
Therefore, the solution to the simultaneous equations using the elimination method is \( \boxed{(4, 2)} \).
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