Question

Find the solution for the following pair of equations
$4x+5y=-4$
$3x-2y=-3$

• A. $(1,3)$
• B. $(-1,0)$
• C. $(2,\frac{9}{2})$
• D. $(0,0)$

Answer 1

The correct option is B $(-1,0)$

Given pair of equations
$4x+5y=-4\dots \left(i\right)$
and $3x-2y=-3\dots \left(ii\right)$

Step 1: Find the value of x
$2\times \left(i\right)\to 8x+10y=-8$
$5\times \left(ii\right)\to 15x-10y=-15$
$2\times \left(i\right)+5\times \left(ii\right)\Rightarrow 8x+10y+15x-10y=-8+(-15)\Rightarrow 23x=-23$
Dividing by $23$ on both the sides, we get
$\Rightarrow x=-1$

Step 2: Find the value of y
Putting $x=-1$ in $\left(i\right),$ we get
Equation $\left(i\right)\to 4\left(x\right)+5y=-4$
$4(-1)+5y=-4\Rightarrow -4+5y=-4$
adding by $4$ on both sides
$\Rightarrow 5y=0$
Dividing by $5$ on both the sides, we get
$\Rightarrow y=0$
$\therefore x=-1,y=0$
$\therefore$ Required solution for the given equations is $(-1,0).$