Question

solve the following system of equations.
7x + 5y = 17
4x - 3y = -2
x =

y =

Explanation:

Step1: Eliminate a variable (e.g., y)

Multiply the first equation by 3: \(3(7x + 5y)=3\times17\) → \(21x + 15y = 51\).
Multiply the second equation by 5: \(5(4x - 3y)=5\times(-2)\) → \(20x - 15y = -10\).

Step2: Add the two new equations

\((21x + 15y)+(20x - 15y)=51+(-10)\)
Simplify: \(41x = 41\) → \(x = 1\).

Step3: Substitute x into an original equation

Use \(7x + 5y = 17\) with \(x = 1\):
\(7(1)+5y = 17\) → \(7 + 5y = 17\) → \(5y = 10\) → \(y = 2\).

Answer:

\(x = 1\), \(y = 2\)