Q52. - Algebra 2

Question

If $x=y+z$ and $x+y=6$ and $x=10$, then $z=$

$\begin{array}{l}A.4\\ B.8\\ C.14\\ D.16\end{array}$

Step-by-Step Solution

Answer

The value of z is Option C $14$.

Step-1 – Apply the substitution method of solving equations

The algebraic method of substitution involves solving the one of the two equations for one variable in terms of other variable and then substituting the expression so formed for the variable in the second equation.

Step-2 – Substitute the value

It is given that $x=10$, so substitute it in $x+y=6$ to find the value of y.

$\begin{array}{c}x+y=6\\ 10+y=6\\ y=6-10\\ y=-4\end{array}$

Thus, the value of y is $- 4$.

Step-3 – Substitute the value of variable

To find the value of z, substitute $y=-4$ and $x=10$ in the equation $x=y+z$ and then solve for as shown.

$\begin{array}{c}x=y+z\\ 10=-4+z\\ z=10+4\\ z=14\end{array}$

Thus, the value of z is $14$.

Hence, value of z is $14$ and the correct option is Option C.