Question

In the following exercises, determine which ordered pairs are solutions to the given equations.

$5x+y=10$

1. $(5,1)$
   
2. $(2,0)$
   
3. $(4,-10)$
   

Short answer

The solutions of the given equation are:

$b.(2,0)$

$c.(4,-10)$

Step-by-step solution

Step 1. Given information

The equation is $5x+y=10$...........equation (1)

Points are

1. $(5,1)$
2. $(2,0)$
3. $(4,-10)$
   

Part (a) Step 1. Check point 5,1

Substitute $x=5,y=1$ in the L.H.S of equation (1)

L.H.S

.$$\begin{gathered} 5\times 5+1 \\ =25+1 \\ =26 \end{gathered}$$

R.H.S. of equation (1) is 10

Since $26\ne 10$

hence $\left(5,1\right)$is not a solution to the equation.

Part(b) Step 1. To check point (2,0) 

Substitute $x=2,y=0$in L.H.S. of equation (1)

L.H.S.

$$\begin{gathered} =5\times 2+0 \\ =10+0 \\ =10 \end{gathered}$$

R.H.S.$=10$

Since L.H.S.=R.H.S.

Hence $\left(2,0\right)$is solution to the equation.

Part(c) Step 1. To check point (4,-10) 

Substitute $x=4,y=-10$in the L.H.S. of given equation (1)

L.H.S.=

$$\begin{gathered} 5\times 4+(-10) \\ =20-10 \\ =10 \end{gathered}$$

R.H.S.$=10$

Since $L.H.S.=R.H.S.$

Hence $\left(4,-10\right)$is solution to the given equation.