Answer :
Given:
[tex]\begin{gathered} x\text{ + 6y = 29 eqn (1)} \\ 2x\text{ - 4y = -6 eqn (2)} \end{gathered}[/tex]Using Substitution method:
From equation (1):
[tex]x\text{ + 6y = 29}[/tex]Make x the subject of formula:
[tex]x\text{ = -6y + 29}[/tex]Substituting back into equation (2):
[tex]\begin{gathered} 2x\text{ - 4y = -6} \\ 2(-6y\text{ + 29) -4y = -6} \\ -12y\text{ + 58 -4y = -6} \end{gathered}[/tex]Collect like terms:
[tex]\begin{gathered} -12y\text{ - 4y = -6 - 58} \\ -\text{ 16y = -64} \end{gathered}[/tex]Divide both sides by -16:
[tex]\begin{gathered} \frac{-16y}{-16}\text{ = }\frac{-64}{-16} \\ y\text{ = 4} \end{gathered}[/tex]Substituting 4 for y into the equation (1):
[tex]\begin{gathered} x\text{ + 6y = 29} \\ x\text{ }+\text{ 6(4) = 29} \\ x\text{ + 24 = 29} \\ x\text{ = 29 - 24} \\ x\text{ = 5} \end{gathered}[/tex]Hence, the solution to the simultaneous equation is:
x =5, y = 4