Question 461920: Solve the following systems of equations and state if any lines are parallel:
y + 7x + 6 = 0
y = 2x + 30
Answer by algebrahouse.com(1659)   (Show Source):
You can put this solution on YOUR website! "Solve the following systems of equations and state if any lines are parallel:"
y + 7x + 6 = 0 ----> y = -7x - 6 {subtracted 7x and 6 from both sides}
y = 2x + 30
Slope-intercept form is y = mx + b
m is the slope
b is the y-intercept
In y = -7x - 6, the slope is -7
In y = 2x + 30, the slope is 2
Parallel lines have equal slopes,
therefore these lines are not parallel.
Now to solve:
y = -7x - 6 {re-arranged first equation}
y = 2x + 30 {original second equation}
-7x - 6 = 2x + 30 {substituted -7x - 6, in for y, into second equation}
-6 = 9x + 30 {added 7x to both sides}
-36 = 9x {subtracted 30 from both sides}
x = -4 {divided both sides by 9}
y = 2x + 30 {original second equation}
y = 2(-4) + 30 {substituted -4, in for x, into y = 2x + 30}
y = -8 + 30 {multiplied 2 by -4}
y = 22 {combined like terms}
x = -4 and y = 22
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