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43. In the system [tex]\( y = 3x + 5 \)[/tex] and [tex]\( 2x + y = 10 \)[/tex], what is the value of [tex]\( x \)[/tex] after substitution?

A. [tex]\(-1\)[/tex]
B. 2
C. 1
D. 0

Sagot :

GinnyAnsweridn
To find the value of [tex]\( x \)[/tex] in the given system of equations, let's follow a step-by-step substitution method.

We are given:
[tex]\[ y = 3x + 5 \][/tex]
[tex]\[ 2x + y = 10 \][/tex]

First, we'll substitute [tex]\( y \)[/tex] from the first equation into the second equation.

1. Start with the second equation:
[tex]\[ 2x + y = 10 \][/tex]

2. Substitute [tex]\( y \)[/tex] from the first equation [tex]\( y = 3x + 5 \)[/tex]:
[tex]\[ 2x + (3x + 5) = 10 \][/tex]

3. Combine like terms:
[tex]\[ 2x + 3x + 5 = 10 \][/tex]
[tex]\[ 5x + 5 = 10 \][/tex]

4. Subtract 5 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 5x + 5 - 5 = 10 - 5 \][/tex]
[tex]\[ 5x = 5 \][/tex]

5. Divide both sides by 5 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 1 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] after substitution is [tex]\( 1 \)[/tex].

The answer is:
[tex]\[ \boxed{1} \][/tex]
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