what is the solution to this system of linear equations?\n2x + 3y = 3\n7x - 3y = 24\n(2,7)\n(3,-21)\n(3,-1)\n…
what is the solution to this system of linear equations?\n2x + 3y = 3\n7x - 3y = 24\n(2,7)\n(3,-21)\n(3,-1)\n(9,0)
Answer
Explanation:
Step1: Add the two equations
$$ \begin{align*} (2x + 3y)+(7x - 3y)&=3 + 24\ 2x+7x+3y - 3y&=27\ 9x&=27 \end{align*} $$
Step2: Solve for (x)
Divide both sides of (9x = 27) by (9), (x=\frac{27}{9}=3)
Step3: Substitute (x = 3) into the first equation
Substitute (x = 3) into (2x+3y = 3), we get (2\times3+3y=3), which is (6 + 3y=3)
Step4: Solve for (y)
Subtract (6) from both sides: (3y=3 - 6=-3). Then divide both sides by (3), (y=\frac{-3}{3}=-1)
Answer:
((3,-1))