Is (1,-2) a solution to this system of equations? y = -8x + 6, y = 8x - 10
Understand the Problem
The question asks whether the point (1, -2) is a solution to the given system of two linear equations. To determine this, the x and y values of the point (1, -2) need to be substituted into both equations. If the point satisfies both equations making them true, then it is a solution to the system.
Answer
yes
Answer for screen readers
yes
Steps to Solve
- Substitute the point (1, -2) into the first equation
Substitute $x = 1$ and $y = -2$ into the equation $y = -8x + 6$.
$-2 = -8(1) + 6$
- Simplify the first equation
Simplify the right side of the equation.
$-2 = -8 + 6$
$-2 = -2$
The point (1, -2) satisfies the first equation.
- Substitute the point (1, -2) into the second equation
Substitute $x = 1$ and $y = -2$ into the equation $y = 8x - 10$.
$-2 = 8(1) - 10$
- Simplify the second equation
Simplify the right side of the equation.
$-2 = 8 - 10$
$-2 = -2$
The point (1, -2) satisfies the second equation.
- Determine if the point is a solution to the system
Since the point (1, -2) 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. In this case, the point (1, -2) made both equations true when substituted.
Tips
A common mistake is to only check one of the equations. A point must satisfy all equations in the system to be a solution. Also, arithmetic errors when substituting and simplifying are common.
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