Answer: The solution is the point (-14, -54)
Explanation:
When we have a system of linear equations like:
y = a*x + b
y = c*x + d
The solution of this system is the point (x, y) that is a solution for both equations, if we graph the lines, this point would be the point where the lines intersect.
To start with this, we need to find the equations of the lines, we will use the following:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Now, for the first table, we can use the points: (-3, -10) and (0, 2)
The slope of this line is:
a = (2 - (-10))/(0 - (-3)) = 12/3 = 4
then we have:
y = 4*x + b
To find the value of b, we can just replace one of the points in the equation, for example, we can use the point (0, 2), this means that we need to replace x by 0, and y by 2.
2 = 4*0 + b
2 = b
Then the equation for the first table is y = 4*x + 2
For the second table, we can use the points (0, -12) and (3, - 3)
Then the slope is:
a = (-3 - (-12))/(3 - 0) = 9/3 = 3
Then we have:
y = 3*x + c
And to find the value of c, we can do the same as before, now we use the point (0, -12) then:
-12 = 3*0 + c
-12 = c
Then the equation for this line is:
y = 3*x - 12
The system of linear equations is then:
y = 4*x + 2
y = 3*x - 12
To find the solution of the system, we must have that y = y, then we can write:
4*x + 2 = y = 3*x - 12
4*x + 2 = 3*x - 12
Now we can solve this for x.
4*x - 3*x = -12 - 2
x = -14
x = -14
Now we can replace this in one of the equations to find the value of y.
y = 3*(-14) - 12 = -54
Then the solution is the point (-14, -54)