Question

consider the system of equations.
y + 4x = 6
3x + 2y = 7
solve the system of equations.
( , )

Explanation:

Step1: Solve first equation for y

From \( y + 4x = 6 \), we get \( y = 6 - 4x \).

Step2: Substitute y into second equation

Substitute \( y = 6 - 4x \) into \( 3x + 2y = 7 \):
\( 3x + 2(6 - 4x) = 7 \)
Simplify: \( 3x + 12 - 8x = 7 \)
Combine like terms: \( -5x + 12 = 7 \)
Subtract 12: \( -5x = -5 \)
Divide by -5: \( x = 1 \).

Step3: Find y using x=1

Substitute \( x = 1 \) into \( y = 6 - 4x \):
\( y = 6 - 4(1) = 2 \).

Answer:

\((1, 2)\)