To find the value of [tex]\( x \)[/tex] that satisfies the system of equations:
1. [tex]\( 2x + 5y = 35 \)[/tex]
2. [tex]\( x = -10 - 15y \)[/tex]
First, we can substitute the expression for [tex]\( x \)[/tex] from the second equation into the first equation. The second equation gives us [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[ x = -10 - 15y \][/tex]
Now, replace [tex]\( x \)[/tex] in the first equation with the expression [tex]\( -10 - 15y \)[/tex]:
[tex]\[ 2(-10 - 15y) + 5y = 35 \][/tex]
Next, distribute the 2 within the parentheses:
[tex]\[ -20 - 30y + 5y = 35 \][/tex]
Combine like terms:
[tex]\[ -20 - 25y = 35 \][/tex]
To isolate [tex]\( y \)[/tex], first add 20 to both sides:
[tex]\[ -25y = 55 \][/tex]
Now, divide both sides by -25:
[tex]\[ y = \frac{55}{-25} \][/tex]
[tex]\[ y = -\frac{55}{25} \][/tex]
[tex]\[ y = -2.2 \][/tex]
Having determined the value of [tex]\( y \)[/tex], substitute it back into the expression for [tex]\( x \)[/tex] given in the second equation:
[tex]\[ x = -10 - 15(-2.2) \][/tex]
Calculate the value:
[tex]\[ x = -10 + 33 \][/tex]
[tex]\[ x = 23 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that satisfies the system of equations is:
[tex]\[ \boxed{23} \][/tex]
