y = 5x + 2\n3x = -y + 10\nwhat is the solution to the system of equations?\n(-4, -18)\n(-18, -4)\n(7…

Explanation:

Step1: Rearrange the second - equation

Given $3x=-y + 10$, we can rewrite it as $y=-3x + 10$.

Step2: Set the two equations equal to each other

Since $y = 5x+2$ and $y=-3x + 10$, we have $5x+2=-3x + 10$.

Step3: Solve for $x$

Add $3x$ to both sides: $5x+3x+2=-3x+3x + 10$, which simplifies to $8x+2 = 10$. Then subtract 2 from both sides: $8x+2-2=10 - 2$, so $8x=8$. Divide both sides by 8: $x = 1$.

Step4: Solve for $y$

Substitute $x = 1$ into the first equation $y = 5x+2$. Then $y=5\times1+2=7$.

Answer:

D. $(1,7)$