Isolate z: Isolate z in the first equation. 3z - 4y = 2z - 4.5 Subtract 2z from both sides to isolate z on one side: 3z - 2z - 4y = 2z - 2z - 4.5 z - 4y = -4.5Substitute expression for 8y: Substitute the expression for 8y from the second equation into the first equation. We have 8y = 2z + 5 from the second equation. Divide both sides by 2 to find the expression for 4y: 8y / 2 = (2z + 5) / 2 4y = z + 2.5 Now substitute this into the first equation where we have z - 4y: z - 4y = -4.5 z - (z + 2.5) = -4.5Simplify equation and solve: Simplify the equation and solve for z. z - z - 2.5 = -4.5 0z - 2.5 = -4.5 -2.5 = -4.5 This step results in a false statement, indicating a math error has occurred in the previous steps.

Grade 8

Solve multi-step equations with fractional coefficients

Full solution

3z-4y=2z-4.5

8y=2z+5

Isolate $z$ : Isolate $z$ in the first equation. $3z - 4y = 2z - 4.5$ Subtract $2z$ from both sides to isolate $z$ on one side: $3z - 2z - 4y = 2z - 2z - 4.5$ $z - 4y = -4.5$
Substitute expression for $8y$ : Substitute the expression for $8y$ from the second equation into the first equation. $\newline$ We have $8y = 2z + 5$ from the second equation. Divide both sides by $2$ to find the expression for $4y$ : $\newline$ $\frac{8y}{2} = \frac{2z + 5}{2}$ $\newline$ $4y = z + 2.5$ $\newline$ Now substitute this into the first equation where we have $z - 4y$ : $\newline$ $z - 4y = -4.5$ $\newline$ $z - (z + 2.5) = -4.5$
Simplify equation and solve: Simplify the equation and solve for $z$ . $z - z - 2.5 = -4.5$ $0z - 2.5 = -4.5$ $-2.5 = -4.5$ This step results in a false statement, indicating a math error has occurred in the previous steps.