To solve the system using elimination, let's start by rewriting the given equations in a standard form:
1) \( 5x - 5y = -25 \)
2) \( 2x - 10y = -42 \)
Step 1: Simplify the first equation.
Divide the first equation by 5:
\[ x - y = -5 \]
Step 2: Simplify the second equation.
Divide the second equation by 2:
\[ x - 5y = -21 \]
Now we have the system:
1) \( x - y = -5 \)
2) \( x - 5y = -21 \)
Step 3: Eliminate \( x \).
Subtract the first equation from the second equation:
\[ (x - 5y) - (x - y) = -21 - (-5) \]
\[ x - 5y - x + y = -21 + 5 \]
\[ -4y = -16 \]
Solve for \( y \):
\[ y = 4 \]
Step 4: Substitute \( y \) back into the first equation to solve for \( x \).
Substitute \( y = 4 \) into \( x - y = -5 \):
\[ x - 4 = -5 \]
\[ x = -1 \]
So, the solution to the system is \( (x, y) = (-1, 4) \).
Thus, the correct answer is: \((–1, 4)\).
4.
Solve the system using elimination.
5x = –25 + 5y
10y = 42 + 2x
(5, 10)
(–1, 4)
(–1, 2)
(4, –1)
1 answer