Question

find the solution to the following systems of linear equations by using the elimination method.\

$$\begin{cases}3x + 5y = 17\\\\2x + 9y = 17\\end{cases}$$

Explanation:

Step1: Eliminate \(x\) by making coefficients equal

Multiply first equation by 2: \(2(3x + 5y)=2\times17\) → \(6x + 10y = 34\)
Multiply second equation by 3: \(3(2x + 9y)=3\times17\) → \(6x + 27y = 51\)

Step2: Subtract equations to eliminate \(x\)

\((6x + 27y)-(6x + 10y)=51 - 34\)
Simplify: \(17y = 17\)

Step3: Solve for \(y\)

Divide both sides by 17: \(y=\frac{17}{17}=1\)

Step4: Substitute \(y = 1\) into first equation

\(3x + 5(1)=17\) → \(3x + 5 = 17\)

Step5: Solve for \(x\)

Subtract 5: \(3x=17 - 5 = 12\)
Divide by 3: \(x=\frac{12}{3}=4\)

Answer:

\(x = 4\), \(y = 1\)