Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations : $\newline$ $2x+3y=10$ . $\newline$ $4x+7y=21$

View step-by-step help

View step-by-step help

Solve equations involving like terms

Full solution

Q. Solve the system of equations :

\newline

2x+3y=10

.

\newline

4x+7y=21

Write Equations: Write down the system of equations. $\newline$ We have the following system of linear equations: $\newline$ $2x + 3y = 10$ $\newline$ $4x + 7y = 21$
Multiply First Equation: Multiply the first equation by $2$ to prepare for elimination. $\newline$ Multiplying the first equation by $2$ gives us: $\newline$ $4x + 6y = 20$ $\newline$ Now we have: $\newline$ $4x + 6y = 20$ $\newline$ $4x + 7y = 21$
Subtract Equations: Subtract the second equation from the first to eliminate $x$ . $\newline$ $(4x + 6y) - (4x + 7y) = 20 - 21$ $\newline$ This simplifies to: $\newline$ $4x + 6y - 4x - 7y = -1$ $\newline$ Which further simplifies to: $\newline$ $-y = -1$
Solve for y: Solve for y. $\newline$ Divide both sides by $-1$ to get: $\newline$ $y = 1$
Substitute and Solve: Substitute $y = 1$ into the first original equation to solve for $x$ . Using the first equation $2x + 3y = 10$ , we substitute $y$ with $1$ : $2x + 3(1) = 10$ $2x + 3 = 10$
Final Solution: Solve for $x$ . $\newline$ Subtract $3$ from both sides to isolate $2x$ : $\newline$ $2x = 10 - 3$ $\newline$ $2x = 7$ $\newline$ Divide both sides by $2$ to get: $\newline$ $x = \frac{7}{2}$ $\newline$ $x = 3.5$

More problems from Solve equations involving like terms

Question

Write the sentence as an equation.

\newline

138

is equal to the quotient of

w

30

\newline

/

) if you want to use a division sign.

\newline

Posted 2 months ago

Question

\newline

(\frac{2}{7})x= -14

\newline

x =

Posted 3 months ago

Question

(\frac{8}{5})x= 32

Posted 3 months ago

Question

\newline

2+2

\newline

Posted 3 days ago

Question

-27x+18y=54

Posted 4 months ago

Question

\newline

48.5-0.434=

Posted 4 months ago

Question

\newline

96.7-0.163=

Posted 4 months ago

Question

\newline

4.43-0.283=

Posted 4 months ago

Question

\newline

3.05-0.338=

Posted 4 months ago

Question

\newline

6.168-0.432=

Posted 4 months ago