Answer:
x = 1 and y = 1
Step-by-step explanation:
Let's solve your system by substitution.
4x + 5y = 9 ; 4x − 2y = 2
- Solve 4x + 5y = 9 for x:
4x + 5y = 9
4x + 5y + − 5y = 9 + − 5y (Add -5y to both sides)
4x = − 5y + 9
[tex]\frac{4}{x} = \frac{- 5y + 9}{4}[/tex]
[tex]x = \frac{- 5}{4} y + \frac{9}{4}[/tex]
Then Substitute [tex]\frac{- 5}{4} y + \frac{9}{4}[/tex] for x in 4x - 2y = 2
4x − 2y = 2
4([tex]\frac{- 5}{4} y + \frac{9}{4}[/tex]) − 2y = 2
− 7y + 9 = 2 (Simplify both sides of the equation)
− 7y + 9 + − 9 = 2 + − 9 (Add -9 to both sides)
− 7y = − 7
[tex]\frac{- 7y}{- 7} = \frac{- 7}{- 7}[/tex] (Divide both sides by -7)
y = 1
Substitute 1 for y in x = [tex]\frac{- 5}{4} y + \frac{9}{4}[/tex]
[tex]x = \frac{- 5}{4} y + \frac{9}{4}[/tex]
[tex]x = \frac{- 5}{4} (1) + \frac{9}{4}[/tex]
x = 1
So, x = 1 and y = 1
