Question

HELP ! PLEASE examine the system of equations.

Answer 1

The solution is $(x=\frac{-7}{2},\ y=\frac{-13}{2} )$.

Solution:

Given system of equations are

$-3 x+y=4$ ---------- (1)

$-9 x+5 y=-1$ ---------- (2)

To solve the given system of equations by substitution method.

Let us take the equation (1) and find the value of y.

(1) ⇒ $-3 x+y=4$

Add 3x on both sides of the equation, we get

⇒ $y=4+3x$

Substitute y = 4 + 3x in equation (2), we get

$-9 x+5 (4+3x)=-1$

$-9 x+20+15x=-1$

Combine like terms together.

$-9 x+15x=-1-20$

$6x=-21$

Divide by 6 on both sides of the equation.

$x=-\frac{21}{6}$

Divide the numerator and denominator by the common factor 3.

$x=-\frac{21\div3}{6\div3}$

$x=-\frac{7}{2}$

Now, substitute x value in y = 4 + 3x, we get

$y=4+3\left(\frac{-7}{2} \right)$

$y=4+\left(\frac{-21}{2} \right)$

Take LCM of the denominators and make the same.

$y=\frac{8}{2} +\frac{-21}{2}$

$y=\frac{-13}{2}$

Hence the solution is $(x=\frac{-7}{2},\ y=\frac{-13}{2} )$.