Question

х+6y = 292х - 4y = -6i already have y solved, i just need help with “back substituting” to solve for x.y=4

Answer 1

Given:

`\begin{gathered} x\text{ + 6y = 29 eqn (1)} \\ 2x\text{ - 4y = -6 eqn (2)} \end{gathered}`

Using Substitution method:

From equation (1):

`x\text{ + 6y = 29}`

Make x the subject of formula:

`x\text{ = -6y + 29}`

Substituting back into equation (2):

`\begin{gathered} 2x\text{ - 4y = -6} \\ 2(-6y\text{ + 29) -4y = -6} \\ -12y\text{ + 58 -4y = -6} \end{gathered}`

Collect like terms:

`\begin{gathered} -12y\text{ - 4y = -6 - 58} \\ -\text{ 16y = -64} \end{gathered}`

Divide both sides by -16:

`\begin{gathered} (-16y)/(-16)\text{ = }(-64)/(-16) \\ y\text{ = 4} \end{gathered}`

Substituting 4 for y into the equation (1):

`\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}`

Hence, the solution to the simultaneous equation is:

x =5, y = 4