Question

Solve the following equations by first combining like terms. a. \(15 x-21 x=-30\) b. \(-13 y-7 y=180\) c. \(-14 x+7 x=42\) d. \(6 y-10 y=64\)

Short answer

Answer: a. x = 5 b. y = -9 c. x = -6 d. y = -16

Step-by-step solution

Combine like terms

For each equation, sum the terms that are multiples of the same variable: a. \((15x-21x)=-30\) \(\Rightarrow -6x=-30\) b. \((-13y-7y)=180\) \(\Rightarrow -20y=180\) c. \((-14x+7x)=42\) \(\Rightarrow -7x=42\) d. \((6y-10y)=64\) \(\Rightarrow -4y=64\)

Divide both sides by the coefficient of the variable

Next, we need to isolate the variable by dividing both sides of the equation by the coefficient (the number multiplying it): a. \(\frac{-6x}{-6}=\frac{-30}{-6}\) \(\Rightarrow x=5\) b. \(\frac{-20y}{-20}=\frac{180}{-20}\) \(\Rightarrow y=-9\) c. \(\frac{-7x}{-7}=\frac{42}{-7}\) \(\Rightarrow x=-6\) d. \(\frac{-4y}{-4}=\frac{64}{-4}\) \(\Rightarrow y=-16\) Finally, we have the values of the variables that satisfy each equation: a. \(x=5\) b. \(y=-9\) c. \(x=-6\) d. \(y=-16\)