Is (-9, 6) a solution to the following system of equations? 7x - 14y = -5 6x + 6y = -18
Understand the Problem
The question asks to verify whether the point (-9, 6) is a solution to the given system of linear equations. We need to substitute x = -9 and y = 6 into both equations and check if both equations holds true. If both equations are true, then (-9, 6) is a solution; otherwise, it is not.
Answer
no
Answer for screen readers
no
Steps to Solve
- Substitute the point (-9, 6) into the first equation
Substitute $x = -9$ and $y = 6$ into the equation $7x - 14y = -5$. $$7(-9) - 14(6) = -5$$ Simplify the left side: $$-63 - 84 = -5$$ $$-147 = -5$$ This equation is not true.
- Substitute the point (-9, 6) into the second equation
Substitute $x = -9$ and $y = 6$ into the equation $6x + 6y = -18$. $$6(-9) + 6(6) = -18$$ Simplify the left side: $$-54 + 36 = -18$$ $$-18 = -18$$ This equation is true.
- Determine if (-9, 6) is a solution
Since the point (-9, 6) does not satisfy both equations, it is not a solution to the system of equations.
no
More Information
A point is a solution to a system of equations if it satisfies all equations in the system. In this case, (-9, 6) satisfies the second equation, but not the first. Therefore, it is not a solution to the system.
Tips
A common mistake is to only check one equation or to make a calculation error when substituting and simplifying. To avoid this, carefully substitute the values into each equation and double-check your arithmetic. Another mistake could also be thinking that the point is a solution if it satisfies one of the equations, instead of both.
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