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Chapter 6: Problem 95

Evaluate \(x^{2}-(x y-y)\) for \(x\) satisfying \(\frac{x}{5}-2=\frac{x}{3}\) and \(y\) satisfying \(-2 y-10=5 y+18\).

Short Answer

Expert verified
The value of the expression \(x^{2}-(x y-y)\) given the conditions is 196.

Step by step solution

01

Solve for x

To find the value of \(x\), we need to solve the equation \(\frac{x}{5}-2=\frac{x}{3}\). First we'll clear the fractions by multiplying everything by 15 (which is the least common multiple of 5 and 3). This gives \(3x - 30 = 5x\). Rearranging the equation, we have \(2x = 30\), which implies that \(x = 15\).
02

Solve for y

To find the value of \(y\), we need to solve the equation \(-2 y-10=5 y+18\). Adding 2y to both sides simplifies to \(-10 = 7y + 18\). Subtracting 18 from both sides gives \(-28 = 7y\). Dividing both sides by 7 we find \(y = -4\).
03

Substitute x and y into expression

The final step in solving the given exercise is substituting the values of \(x\) and \(y\) into the expression \(x^{2}-(x y-y)\). Substituting \(x = 15\) and \(y = -4\) we get \(15^{2}-((15*-4)-(-4))\). The result of the operation is 196.

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Most popular questions from this chapter

Solve the equations using the quadratic formula. \(x^{2}-5 x=10\)

Solve the quadratic equations by factoring. \(x(6 x+13)+6=0\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I solved \(-2 x+5 \geq 13\) and concluded that \(-4\) is the greatest integer in the solution set.

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(3 x^{2}-x-2\)

Solve the equations in Exercises 53-72 using the quadratic formula. \(x^{2}+8 x+15=0\)
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