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What value of [tex]\( x \)[/tex] satisfies the system of equations?

[tex]\[
\begin{cases}
2x + 5y = 35 \\
x = -10 - 15y
\end{cases}
\][/tex]

Enter your answer as the correct value for [tex]\( x \)[/tex].

Sagot :

GinnyAnsweridn
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]
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