Question

solve the system by substitution.\\(4x - 2y = 14\\)\\(y = \frac{1}{2}x - 1\\)\\(\text{the solution is }(\square, \square).\\)

Explanation:

Step1: Substitute \( y \) into the first equation

We know \( y = \frac{1}{2}x - 1 \), substitute this into \( 4x - 2y = 14 \).
So we get \( 4x - 2(\frac{1}{2}x - 1) = 14 \).

Step2: Simplify the equation

First, expand the left - hand side:
\( 4x - 2\times\frac{1}{2}x+2\times1 = 14 \)
\( 4x - x + 2 = 14 \)
Combine like terms: \( 3x+2 = 14 \)

Step3: Solve for \( x \)

Subtract 2 from both sides of the equation: \( 3x+2 - 2=14 - 2 \), which simplifies to \( 3x = 12 \)
Divide both sides by 3: \( x=\frac{12}{3}=4 \)

Step4: Solve for \( y \)

Substitute \( x = 4 \) into the equation \( y=\frac{1}{2}x - 1 \)
\( y=\frac{1}{2}\times4-1 \)
\( y = 2 - 1=1 \)

Answer:

\((4,1)\)