Solve the equations y = 8x - 10 and y = 2x + 2.
Understand the Problem
The question is asking us to solve a system of equations involving two linear equations represented in the form of y = mx + b. We will equate the two equations and solve for x first, and then use the value of x to find y.
Answer
The solution is \( (2, 6) \).
Answer for screen readers
The solution is ( (2, 6) ).
Steps to Solve
- Set the equations equal to each other
Since both equations equal ( y ), we can set them equal to each other:
$$ 8x - 10 = 2x + 2 $$
- Isolate the variable ( x )
To solve for ( x ), first, subtract ( 2x ) from both sides:
$$ 8x - 2x - 10 = 2 $$
This simplifies to:
$$ 6x - 10 = 2 $$
- Add 10 to both sides
Next, add 10 to both sides of the equation:
$$ 6x = 12 $$
- Solve for ( x )
Now, divide both sides by 6 to find ( x ):
$$ x = 2 $$
- Substitute ( x ) back into one of the original equations
We can substitute ( x = 2 ) back into one of the original equations. We'll use the second equation:
$$ y = 2x + 2 $$
Substituting in ( x ):
$$ y = 2(2) + 2 = 4 + 2 = 6 $$
- Write the final solution
The solution to the system of equations is:
$$ (x, y) = (2, 6) $$
The solution is ( (2, 6) ).
More Information
This solution means that the lines represented by the two equations intersect at the point ( (2, 6) ). This point is the only point where both equations are satisfied simultaneously.
Tips
- Forgetting to combine like terms when simplifying the equations.
- Failing to check the solution by substituting it back into both original equations.
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