Is (-5, -8) a solution to the system of equations y = 3x + 7 and y = 2x + 2?
Understand the Problem
The question asks if the point (-5, -8) is a solution to the system of equations y = 3x + 7 and y = 2x + 2. To determine this, we need to substitute x = -5 and y = -8 into both equations and check if the equations hold true.
Answer
yes
Answer for screen readers
yes
Steps to Solve
- Substitute the point into the first equation
Substitute $x = -5$ and $y = -8$ into the first equation $y = 3x + 7$: $$ -8 = 3(-5) + 7 $$ $$ -8 = -15 + 7 $$ $$ -8 = -8 $$ The first equation holds true.
- Substitute the point into the second equation
Substitute $x = -5$ and $y = -8$ into the second equation $y = 2x + 2$: $$ -8 = 2(-5) + 2 $$ $$ -8 = -10 + 2 $$ $$ -8 = -8 $$ The second equation also holds true.
- Determine if the point is a solution
Since the point $(-5, -8)$ satisfies both equations, it is a solution to the system of equations.
yes
More Information
A solution to a system of equations is a point that satisfies all equations in the system.
Tips
A common mistake is to only check one of the equations. The point must satisfy all equations in the system to be a solution. Another common mistake is to incorrectly perform the arithmetic when substituting and evaluating the equations.
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