Answered

Join IDNLearn.com to access a wealth of knowledge and get your questions answered by experts. Our community is here to provide the comprehensive and accurate answers you need to make informed decisions.

Solve the system of equations:

[tex]\[
\begin{cases}
y = 3x - 5 \\
x - 4y + 2 = 0
\end{cases}
\][/tex]

Sagot :

GinnyAnsweridn
Sure, let's solve the system of equations step by step:

We have the system of equations:
[tex]\[ \begin{cases} y = 3x - 5 \\ x - 4y + 2 = 0 \end{cases} \][/tex]

Step 1: Solve the first equation for [tex]\( y \)[/tex]:
[tex]\[ y = 3x - 5 \][/tex]

Step 2: Substitute [tex]\( y \)[/tex] from the first equation into the second equation:
[tex]\[ x - 4(3x - 5) + 2 = 0 \][/tex]

Step 3: Simplify the expression inside the parentheses:
[tex]\[ x - 12x + 20 + 2 = 0 \][/tex]

Step 4: Combine like terms:
[tex]\[ -11x + 22 = 0 \][/tex]

Step 5: Solve for [tex]\( x \)[/tex]:
[tex]\[ -11x = -22 \][/tex]
[tex]\[ x = \frac{-22}{-11} \][/tex]
[tex]\[ x = 2 \][/tex]

Step 6: Substitute [tex]\( x = 2 \)[/tex] back into the first equation to find [tex]\( y \)[/tex]:
[tex]\[ y = 3(2) - 5 \][/tex]
[tex]\[ y = 6 - 5 \][/tex]
[tex]\[ y = 1 \][/tex]

So, the solution to the system of equations is:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = 1 \][/tex]

Hence, the solution is:
[tex]\[ (x, y) = (2, 1) \][/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.