solve the system using multiplication for the linear combination method.\n6x - 3y = 3\n-2x + 6y = 14\nwhat…

solve the system using multiplication for the linear combination method.\n6x - 3y = 3\n-2x + 6y = 14\nwhat is the solution to the system?\n(2, 1)\n(2, -3)\n(2, -1)\n(2, 3)

solve the system using multiplication for the linear combination method.\n6x - 3y = 3\n-2x + 6y = 14\nwhat is the solution to the system?\n(2, 1)\n(2, -3)\n(2, -1)\n(2, 3)

Answer

Explanation:

Step1: Multiply second - equation to eliminate x

Multiply the second equation $-2x + 6y=14$ by 3. We get $-6x+18y = 42$.

Step2: Add the two equations

Add $6x - 3y=3$ and $-6x + 18y=42$: $$(6x-3y)+(-6x + 18y)=3 + 42$$ $$6x-3y-6x + 18y=45$$ $$15y=45$$

Step3: Solve for y

Divide both sides of $15y = 45$ by 15. So $y=\frac{45}{15}=3$.

Step4: Substitute y into first equation

Substitute $y = 3$ into the first equation $6x-3y = 3$. We have $6x-3\times3=3$, which simplifies to $6x-9 = 3$.

Step5: Solve for x

Add 9 to both sides: $6x=3 + 9=12$. Then divide both sides by 6, so $x=\frac{12}{6}=2$.

Answer:

D. $(2,3)$