Textbook Question
Simplify each expression. See Example 8. 10x (3)(y)
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0. Review of College Algebra
Solving Linear Equations
Multiple Choice
Given the equations of two lines and , determine whether the lines intersect. If they do, find the point of intersection.
A
Yes, the lines intersect at
B
No, the lines are parallel and do not intersect.
C
Yes, the lines intersect at
D
Yes, the lines intersect at
Verified step by step guidance1
Identify the two given lines: Line 1 is \(y = 2x + 1\) and Line 2 is \(y = -x + 4\).
To find if the lines intersect, set their right-hand sides equal to each other because at the point of intersection, both lines have the same \(x\) and \(y\) values. So, solve the equation \$2x + 1 = -x + 4$.
Rearrange the equation to isolate \(x\): add \(x\) to both sides and subtract 1 from both sides to get \$3x = 3$.
Solve for \(x\) by dividing both sides by 3, which gives \(x = 1\).
Substitute \(x = 1\) back into either original equation to find the corresponding \(y\) value. For example, using \(y = 2x + 1\), calculate \(y = 2(1) + 1\).
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