Question

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$$\begin{cases} 3x + 4y = 7 \\\\ -2x + y = 10 \\end{cases}$$

Explanation:

Step1: Solve the second equation for y

From \(-2x + y = 10\), we can express \(y\) in terms of \(x\) by adding \(2x\) to both sides. So, \(y = 2x + 10\).

Step2: Substitute y into the first equation

Substitute \(y = 2x + 10\) into \(3x + 4y = 7\). We get \(3x + 4(2x + 10) = 7\).

Step3: Simplify and solve for x

First, expand the equation: \(3x + 8x + 40 = 7\). Combine like terms: \(11x + 40 = 7\). Subtract 40 from both sides: \(11x = 7 - 40 = -33\). Then divide both sides by 11: \(x = \frac{-33}{11} = -3\).

Step4: Substitute x back to find y

Substitute \(x = -3\) into \(y = 2x + 10\). So, \(y = 2(-3) + 10 = -6 + 10 = 4\).

Answer:

The solution to the system of equations is \(x = -3\) and \(y = 4\)