What is the $x$-value in the solution to this system of linear equations?
[tex]
\begin{array}{l}
2 x-y=11 \\
x+3 y=-5
\end{array}
[/tex]
Answer (1)
To find the x -value in the solution to the system of linear equations given by:
2 x − y = 11 x + 3 y = − 5
we can use the method of substitution or elimination. I will demonstrate the elimination method step-by-step:
Align the equations:
The given system is:
( 1 ) 2 x − y = 11
( 2 ) x + 3 y = − 5
Eliminate one variable:
We can eliminate y by making the coefficients of y the same in both equations. We do this by multiplying equation (1) by 3:
3 ( 2 x − y ) = 3 ( 11 )
which simplifies to:
6 x − 3 y = 33
Our system now looks like:
( 3 ) 6 x − 3 y = 33
( 2 ) x + 3 y = − 5
Add the equations:
Add equations (2) and (3) to eliminate y :
( 6 x − 3 y ) + ( x + 3 y ) = 33 + ( − 5 )
Simplifying gives:
7 x = 28
Solve for x :
Divide both sides by 7:
x = 4
Thus, the x -value in the solution to this system of equations is x = 4 .
