Question

Solve this system. Write your answer as an ordered pair.

-5x + y = -3

3x - 8y = 24

Answer 1

`\begin{cases} -5x+y=-3\\ 3x-8y=24 \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{-5x+y=-3}\implies \underline{y=-3+5x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{3x-8(\underset{y}{-3+5x})=24}\implies 3x+24-40x=24\implies 3x-40x=0 \\\\\\ -37x=0\implies \boxed{x=0}~\hfill \underline{y=-3+5(\stackrel{x}{0})}\implies \boxed{y=-3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-3)~\hfill`

Answer 2

( 0, -3 )

Explanation:

-5x + y = -3 ⇒ ( 1 )

3x - 8y = 24 ⇒ ( 2 )

We can make y the subject of equation 1.

y = 5x - 3 ⇒ ( 3 )

Now let us take equation 2.

Here we can replace y with ( 5x - 3 ) to find the value of x.

Value of x.

3x - 8y = 24

3x - 8 (5x - 3) = 24

3x - 40x + 24 = 24

-37x = 0

x = 0

Now let us take equation 3 to find the value of y.

Here we can replace x with 0.

Let us find it now.

y = 5x - 3

y = 5 × 0 - 3

y = 0 - 3

y = -3

Now, let us write the answer as an ordered pair.

( x, y )

( 0, -3 )