Question

Solve the following system of equations using the Substitution Method. Use the infinity symbol if infinitelymany solutions exist, or enter DNE if there are no solutions.4x + 5y = 35x – 2y = -1

Answer 1

The system of equations is given to be:

`\begin{gathered} 4x+5y=35\text{ ----------------(1)} \\ x-2y=-1\text{ ---------------(2)} \end{gathered}`

Step 1: Make x the subject of the formula in equation (2)

`x=2y-1\text{ ---------------(3)}`

Step 2: Substitute for x as calculated in equation (3) into equation (1)

`4(2y-1)+5y=35`

Step 3: Solve the equation from Step 2

`\begin{gathered} 8y-4+5y=35 \\ 13y=35+4 \\ 13y=39 \\ y=(39)/(13) \\ y=3 \end{gathered}`

Step 4: Substitute the value of y into equation (3) to get x

`\begin{gathered} x=2(3)-1 \\ x=6-1 \\ x=5 \end{gathered}`

SOLUTION

`(x,y)=(5,3)`