Question

How many solutions does this system have?
2 x +3y = -3
3x + 5 = -9

Answer 1

Answer:

x = 12 and y = -9

                                            Explanation:

Given:

2 x +3y = -3

3x + 5y = -9

make x the subject:

$2 x +3y = -3$

$2x = -3 - 3y$

$x = \frac{-3 - 3y}{2}$ _____equation 1

$3x + 5y = -9$

$3x = -9-5y$

$x = \frac{-9-5y}{3}$ ______equation 2

solve them simultaneously:

$\frac{-9-5y}{3} = \frac{-3 - 3y}{2}$

$2(-9-5y) = 3(-3-3y)$

$-18-10y = -9 - 9y$

$-10y + 9y = -9 + 18$

$-y = 9$

$y = -9$

now solve for x:

$2 x +3y = -3$

$2x + 3(-9) = -3$

$2x -27 = -3$

$2x = -3 + 27$

$2x = 24$

$x = 12$

coordinates where they both intersect is (12,-9) at one point so they have one solution

Answer 2

Answer:

x = 12

y = -9

The system has one solution as it has one point of intersection at (12, -9)

Step-by-step explanation:

Equation 1:   $2x + 3y = -3$

Equation 2:   $3x + 5y = -9$

Rewrite equation 1 to make $x$ the subject:

       $2x + 3y = -3$

$\implies 2x = -3 - 3y$

$\implies x = -\dfrac32 - \dfrac32 y$

Substitute this into equation 2 and solve for $y$:

       $3( -\dfrac32 - \dfrac32 y)+5y=-9$

$\implies -\dfrac92 - \dfrac92 y+5y=-9$

$\implies -\dfrac92 +\dfrac12 y=-9$

$\implies \dfrac12 y=-\dfrac92$

$\implies y=-9$

Substitute y = -9 into one of the equations to find $x$:

      $2x + 3(-9) = -3$

$\implies 2x - 27 = -3$

$\implies 2x = 24$

$\implies x=12$