Answer:
[tex]x = -\frac{9}{2} , y = 5[/tex]
Step-by-step explanation:
1. Solve 2x + 6y = 21 for x.
Step 1: Add -6y to both sides
- [tex]2x + 6y - 6y = 21 -6y[/tex]
- [tex]2x = -6y + 21[/tex]
Step 2: Divide both sides by 2.
- [tex]\frac{2x}{2} = \frac{-6y+21}{2}[/tex]
- [tex]x = -3y + \frac{21}{2}[/tex]
2. Substitute -3y + 21/2 for x in -2x + 3y = 24.
Step 1: Simplify both sides of the equation.
- [tex]-2(-3y+\frac{21}{2}) + 3y = 24[/tex]
- [tex]9y - 21 = 24[/tex]
Step 2: Add 21 to both sides.
- [tex]9y - 21 + 21 = 24 + 21[/tex]
- [tex]9y = 45[/tex]
Step 3: Divide both sides by 9.
- [tex]\frac{9y}{9} = \frac{45}{0}[/tex]
- [tex]y = 5[/tex]
3. Substitute 5 for y in x = -3y + 21/2
Step 1: Simplify both sides of the equation.
- [tex]x = -3y + \frac{21}{2}[/tex]
- [tex]x = -3(5) + \frac{21}{2}[/tex]
- [tex]x = -15 + \frac{21}{2}[/tex]
- [tex]x = -\frac{9}{2}[/tex]
Therefore, x = -9/2 and y = 5.
