The solution to the system of equations is: (1, -8).
How to Find the Solution to a System of Equations?
The solution is the coordinate of the point where both lines of the equations meet.
Second equation: 3y + 30 = 6x, rewrote in slope-intercept form:
3y = 6x - 30
y = 6x/3 - 30/3
y = 2x - 10 --> eqn. 1
Find the slope (m) and y-intercept (b) of the first graphed equation:
Slope (m) = change in y/change in x = rise/run = -4/2 = -2
The line intersects the y-axis at y = -6, so, the y-intercept, b = -6.
The first equation would be: y = -2x - 6 ---> eqn. 2
Subtract eqn. 2 from eqn. 1 to eliminate x
y = 2x - 10 --> eqn. 1
y = -2x - 6 ---> eqn. 2
2y = 0 - 16
2y = -16
y = -16/2
y = -8
Substitute y = -8 into eqn. 1 to find x:
-8 = 2x - 10
-8 + 10 = 2x
2 = 2x
2/2 = x
1 = x
x = 1
The solution is therefore: (1, -8).
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