Answer: (-4, -7)
Step-by-step explanation: To solve this system of equations, we can use the substitution method.
To solve a system by substitution, we first need to isolate one of our variables. The problem is none of our variables has a coefficient of 1 or -1. In this situation, we have to look at our next best option.
In our first equation, add 2x to both sides to get
2y = -6 + 2x and just divide both sides by 2 to get y = -3 + x.
Now let's plug this value of y into our second equation.
So we have 3x + 7(-3 + x) = -61.
Simplifying from here:
3x - 21 + 7x = -61
10x - 21 = -61
10x = -40
x = -4
Since we know that x = -4, we can just plug a -4 into our equation that we created earlier to get y = -3 + (-4) or y = -7.
Since x = -4 and y = -7, our answer is the ordered pair (-4, -7).