Question

question 9
solve the system using addition/elimination method. if there is exactly one solution, write as an ordered pair. if not, choose one of the other options.
{5x + 3y = -19
-3x + 2y = 19
one solution:
no solution
infinite number of solutions
question help: video 1 video 2
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Explanation:

Step1: Multiply equations to eliminate x

Multiply the first equation $5x + 3y=-19$ by 3 and the second equation $-3x + 2y = 19$ by 5.
The first - new equation is $3(5x + 3y)=3\times(-19)\Rightarrow15x+9y=-57$.
The second - new equation is $5(-3x + 2y)=5\times19\Rightarrow-15x + 10y = 95$.

Step2: Add the two new equations

$(15x+9y)+(-15x + 10y)=-57 + 95$.
Combining like - terms, we get $(15x-15x)+(9y + 10y)=38$, so $19y = 38$.
Solve for y: $y=\frac{38}{19}=2$.

Step3: Substitute y into one of the original equations

Substitute $y = 2$ into the first original equation $5x+3y=-19$.
We have $5x+3\times2=-19$.
$5x+6=-19$.
Subtract 6 from both sides: $5x=-19 - 6=-25$.
Solve for x: $x=\frac{-25}{5}=-5$.

Answer:

$(-5,2)$