Question

solve the system of linear equations by substitution. enter your answer as an ordered pair.\

$$\begin{cases}7x + 4y = -40\\\\3x - 4y = -40\\end{cases}$$

Explanation:

Step1: Solve one equation for a variable

Let's solve the second equation \(3x - 4y = -40\) for \(4y\).
\(3x - 4y = -40\)
Subtract \(3x\) from both sides: \(-4y = -40 - 3x\)
Multiply both sides by -1: \(4y = 40 + 3x\)

Step2: Substitute into the first equation

Substitute \(4y = 40 + 3x\) into the first equation \(7x + 4y = -40\).
\(7x + (40 + 3x) = -40\)
Combine like terms: \(10x + 40 = -40\)

Step3: Solve for x

Subtract 40 from both sides: \(10x = -40 - 40\)
\(10x = -80\)
Divide both sides by 10: \(x = \frac{-80}{10} = -8\)

Step4: Substitute x back to find y

Now substitute \(x = -8\) into \(4y = 40 + 3x\).
\(4y = 40 + 3(-8)\)
\(4y = 40 - 24\)
\(4y = 16\)
Divide both sides by 4: \(y = \frac{16}{4} = 4\)

Answer:

\((-8, 4)\)