Solve:

y=3x+7
y=4x-2

3x+7=4x-2

solve for x

To solve the system of equations:

Step 1: Set the two expressions for y equal to each other since they both represent y.
3x + 7 = 4x - 2

Step 2: Simplify the equation by combining like terms. In this case, we can subtract 3x from both sides to isolate the x terms on one side of the equation.
7 = 4x - 3x - 2

Step 3: Continue simplifying by combining like terms.
7 = x - 2

Step 4: Isolate the x term by adding 2 to both sides of the equation.
9 = x

Step 5: Substitute the value of x back into either of the original equations to find the value of y. Let's use the first equation:
y = 3(9) + 7
y = 27 + 7
y = 34

Therefore, the solution to the system of equations is x = 9 and y = 34.