Question

Use the given values to complete each table (sorry the image is tipped)

Answer 1

(2) The solutions are $-10,-2,6$

(3) The solutions are $20,\frac{5}{2} ,32$

Explanation:

(2) The value of the equation $2z-a$ can be found by substituting the values for z and a.

For $z=-4$ and $a=2$, we get,

$\begin{aligned}2 z-a &=2(-4)-2 \\&=-8-2 \\&=-10\end{aligned}$

For $z=0$ and $a=2$, we get,

$\begin{aligned}2 z-a &=2(0)-2 \\&=0-2 \\&=-2\end{aligned}$

For $z=4$ and $a=2$, we get,

$\begin{aligned}2 z-a &=2(4)-2 \\&=8-2 \\&=6\end{aligned}$

Thus, the solutions are $-10,-2,6$

(3) The value of the equation $10 x^{2} \div(y+1)$ can be found by substituting the values for x and y.

For $x=2$ and $y=1$, we get,

$\begin{aligned}10 x^{2} \div(y+1) &=10(2)^{2} \div(1+1) \\&=10(4) \div(2) \\&=40 \div 2 \\&=20\end{aligned}$

For $x=-1$ and $y=3$, we get,

$\begin{aligned}10 x^{2} \div(y+1) &=10(-1)^{2} \div(3+1) \\&=10(1) \div(4) \\&=10 \div 4 \\&=\frac{5}{2} \end{aligned}$

For $x=-4$ and $y=4$, we get,

$\begin{aligned}10 x^{2} \div(y+1) &=10(-4)^{2} \div(4+1) \\&=10(16) \div(5) \\&=160 \div 5 \\&=32 \end{aligned}$

Thus, the solutions are $20,\frac{5}{2} ,32$