Solve the system of equations.
3x+y=2
7x−4y=30
To solve this system of equations, we can use the method of substitution or elimination.
Let's first solve the first equation for y:
3x + y = 2
y = 2 - 3x
Now substitute this expression for y into the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2
Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:
3(2) + y = 2
6 + y = 2
y = -4
Therefore, the solution to the system of equations is x = 2 and y = -4.