Answer: the solution to the system of equations is approximately (3.5, 2.25)
Explanation:
The first equation can be rewritten in the form y = mx + b, where m is the slope and b is the y-intercept, by solving for y:
-3x + 2y = -6
2y = 3x + 6
y = (3/2)x + 3
The second equation already has the form y = mx + b:
y = -1/2 x + 4
Now that both equations are in the form y = mx + b, we can graph them on a coordinate plane and find the point at which they intersect, which is the solution to the system. The x and y coordinates of the intersection point are the values that satisfy both equations simultaneously.
The x and y values of the intersection point can be found either by solving for x and y or by using the method of substitution.
By using substitution, we can substitute the value of y from the second equation into the first equation to solve for x:
-3x + 2(-1/2 x + 4) = -6
-3x + (-x + 8) = -6
-4x + 8 = -6
-4x = -14
x = 3.5
Now that we have found x, we can substitute it into either equation to find y:
y = -1/2 x + 4
y = -1/2 * 3.5 + 4
y = 2.25
So, the solution to the system of equations is approximately (3.5, 2.25).