Question

(d) 8x + 3y = -4 5x + 2y = 6

Answer 1

We are given two equations involving x and y

`\begin{gathered} 8x+3y=-4\text{ eq. 1} \\ 5x+2y=6\text{ eq. 2} \end{gathered}`

We want to solve these equations and find out the values of x and y.

We can use the substitution method to solve these equations.

`\begin{gathered} 5x+2y=6 \\ 2y=6-5x \\ y=(6-5x)/(2)\text{ eq. 3} \end{gathered}`

Substitute eq. 3 into eq. 1 and then simplify.

`\begin{gathered} 8x+3y=-4 \\ 8x+3((6-5x)/(2))=-4 \\ 8x+(18-15x)/(2)=-4 \\ (2(8x)+18-15x)/(2)=-4 \\ 16x+18-15x=-8 \\ 16x-15x=-8-18 \\ x=-26 \end{gathered}`

So we have found the value of x.

Now substitute the value of x into eq. 3 to get the value of y.

`\begin{gathered} y=(6-5x)/(2) \\ y=(6-5(-26))/(2) \\ y=(6+130)/(2) \\ y=(136)/(2) \\ y=68 \end{gathered}`

So we have found the value of y.

Therefore, the solution is

`\begin{gathered} x=-26 \\ y=68 \end{gathered}`