use elimination to solve the system of equations.\n$7x + 5y = -21$\n$-4x + 2y = 12$
use elimination to solve the system of equations.\n$7x + 5y = -21$\n$-4x + 2y = 12$
Answer
Explanation:
Step1: Eliminate y (scale equations)
To eliminate ( y ), we can make the coefficients of ( y ) opposites. Multiply the first equation ( 7x + 5y = -21 ) by ( 2 ) and the second equation ( -4x + 2y = 12 ) by ( 5 ):
First equation: ( 2(7x + 5y) = 2(-21) ) → ( 14x + 10y = -42 )
Second equation: ( 5(-4x + 2y) = 5(12) ) → ( -20x + 10y = 60 )
Step2: Subtract to eliminate y
Subtract the second new equation from the first to eliminate ( y ):
( (14x + 10y) - (-20x + 10y) = -42 - 60 )
Simplify: ( 14x + 10y + 20x - 10y = -102 ) → ( 34x = -102 )
Step3: Solve for x
Divide both sides by ( 34 ):
( x = \frac{-102}{34} = -3 )
Step4: Substitute x to find y
Substitute ( x = -3 ) into the second original equation ( -4x + 2y = 12 ):
( -4(-3) + 2y = 12 ) → ( 12 + 2y = 12 )
Subtract ( 12 ) from both sides: ( 2y = 0 ) → ( y = 0 )
Answer:
( (-3, 0) )