Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$3z-4y=2z-4.5$ and $8y=2z+5$ . solve for $z$

View step-by-step help

View step-by-step help

Solve linear equations

Full solution

Q.

3z-4y=2z-4.5

and

8y=2z+5

. solve for

z

Isolate z in Equation: First, let's isolate z in the second equation. $\newline$ $8y = 2z + 5$ $\newline$ Subtract $2z$ from both sides to get z by itself. $\newline$ $8y - 2z = 5$ $\newline$ Now, divide both sides by $2$ to solve for z. $\newline$ $(8y - 2z) / 2 = 5 / 2$ $\newline$ $4y - z = 2.5$ $\newline$ Now we have an expression for z in terms of y.
Express $z$ from First Equation: Next, let's express $z$ from the first equation. $\newline$ $3z - 4y = 2z - 4.5$ $\newline$ Subtract $2z$ from both sides to isolate $z$ . $\newline$ $3z - 2z - 4y = -4.5$ $\newline$ $z - 4y = -4.5$ $\newline$ Now we have another expression for $z$ in terms of $y$ .
Set Equations Equal: We can now set the two expressions for $z$ equal to each other since they both equal $z$ . $4y - z = 2.5$ $z - 4y = -4.5$ Add $z$ to both sides of the second equation and add $4y$ to both sides to get the $z$ terms on one side and the constants on the other. $4y - z + z = 2.5 + z$ $z - 4y + 4y = -4.5 + 4y$ Simplifying both equations, we get: $4y = 2.5 + z$ $z$ $0$
Substitute $4y$ into Second Equation: Now we can substitute $4y$ from the first simplified equation into the second. $z = -4.5 + 4y$ Substitute $4y$ with $2.5 + z$ . $z = -4.5 + (2.5 + z)$ Simplify the equation. $z = -4.5 + 2.5 + z$ $z = -2 + z$
Check for Mistake: We see that we have $z$ on both sides of the equation, which suggests that we may have made a mistake. Let's go back and check our work.

More problems from Solve linear equations

Question

3 n^{2}=27

\newline

What are the solutions to the given equation?

\newline

1

\newline

n=\sqrt{3}

\newline

n=3

\newline

n=-\sqrt{3}

n=\sqrt{3}

\newline

n=-3

n=3

Posted 4 months ago

Question

6=3 x

, what is the value of

x

Posted 1 month ago

Question

9=9 x

, what is the value of

x

Posted 1 month ago

Question

\frac{1}{2} c^{2}+3 c=1

\newline

c=f

c=g

be the solutions to the given equation. If

f>g

, which of the following is the value of

f

\newline

1

\newline

-3+\sqrt{2}

\newline

-3+\sqrt{11}

\newline

3+\sqrt{2}

\newline

3+\sqrt{11}

Posted 1 month ago

Question

Find the value of

x

that solves the equation

\ln (x-3)=1+\ln 2

\newline

Posted 2 months ago

Question

Find the value of

x

that solves the equation

\ln (x-1)+\ln 5=2

\newline

Posted 2 months ago

Question

Find the value of

x

that solves the equation

\ln (x+3)-\ln 2=0

\newline

Posted 2 months ago

Question

Find the value of

x

that solves the equation

\ln (x-3)-3 \ln 4=\ln 10

\newline

x=

Posted 2 months ago

Question

Find the value of `x`

\newline

6x+32=8x-8

Posted 2 months ago

Question

\$200

with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get

40

hats. If Aiden purchases only t-shirts, he will get

80

t-shirts. Which of the following best models the relationship between the number of hats,

h

, and the number of t-shirts,

t

, that Aiden could purchase with this money?

\newline

1

\newline

40h+80t=400

\newline

80h+40t=200

\newline

5h+2.5t=200

\newline

2.5h+5t=200

Posted 2 months ago