Which of the following equations has an infinite number of solutions? (1 point)
3x – 3 = –4x
2y + 4 – y = 16
7x + 5 = 4x + 5 + 3x
6y – 2 = 2(y – 1)
solve for x and y in each equation
a 7x=3, x=3/7 no
b y=12, no
c 7x+5 = 7x+5 => 5=5 YES
d 6y-2 = 2y-2 => 4y=0 y=0 no
i worked it out and then posted the ? to see if i got it rght
cn u help me on this one
4. Graph the inequality: x ≤ –2 (1 point)
To determine which equation has an infinite number of solutions, we need to solve each equation and check if it leads to a contradiction or an identity.
Let's solve each equation step-by-step:
1) 3x – 3 = –4x
Combine like terms:
3x + 4x = 3
7x = 3
Divide both sides by 7:
x = 3/7
2) 2y + 4 – y = 16
Combine like terms:
y + 4 = 16
Subtract 4 from both sides:
y = 16 - 4
y = 12
3) 7x + 5 = 4x + 5 + 3x
Combine like terms:
7x - 4x - 3x = 5 - 5
0x = 0
This equation simplifies to 0 = 0, which is true for any value of x. Hence, it has an infinite number of solutions.
4) 6y – 2 = 2(y – 1)
Distribute the 2 on the right side:
6y – 2 = 2y - 2
Subtract 2y from both sides:
6y - 2y - 2 = 0
4y - 2 = 0
Add 2 to both sides:
4y = 2
Divide both sides by 4:
y = 2/4
y = 1/2
So, out of the four given equations, the equation 7x + 5 = 4x + 5 + 3x has an infinite number of solutions.