Question

solve the system by the elimination method.
$x + 3y = 11$
$3x + 5y = 17$
select the correct choice below and, if necessary, fill in the answer box
a. the solution is (simplify your answer. type an ordered pair.)
b. there are infinitely many solutions
c. there is no solution.

Explanation:

Step1: Eliminate $x$ term.

Multiply first equation by 2: $2(x + 3y) = 2\times11$ → $2x + 6y = 22$
Subtract second equation: $(2x + 6y) - (2x + 5y) = 22 - 17$

Step2: Solve for $y$.

Simplify the equation: $y = 5$

Step3: Substitute $y$ to find $x$.

Plug $y=5$ into $x + 3y = 11$: $x + 3\times5 = 11$ → $x + 15 = 11$
Solve for $x$: $x = 11 - 15 = -4$

Answer:

A. The solution is $(-4, 5)$ (Simplify your answer. Type an ordered pair.)