Question

solve the system of equations by the substitution method.
3x - y = 26
5x + 4y = 32

what is the solution of the system? select the correct choice and, if necessary, fill in the answer box to c
a. the solution is \boxed{}.
(simplify your answer. type an ordered pair.)

b. there are an infinite number of solutions of the form \boxed{}.
(simplify your answer. type an ordered pair. type an expression using y as the variable. use inte

c. there is no solution.

Explanation:

Step1: Solve for y from first equation

From \(3x - y = 26\), we can rewrite it as \(y = 3x - 26\).

Step2: Substitute y into second equation

Substitute \(y = 3x - 26\) into \(5x + 4y = 32\). So we get \(5x + 4(3x - 26)=32\).

Step3: Simplify and solve for x

First, expand the equation: \(5x + 12x - 104 = 32\). Combine like terms: \(17x - 104 = 32\). Add 104 to both sides: \(17x = 32 + 104 = 136\). Then divide both sides by 17: \(x=\frac{136}{17} = 8\).

Step4: Solve for y

Substitute \(x = 8\) into \(y = 3x - 26\). So \(y=3\times8 - 26=24 - 26=-2\).

Answer:

A. The solution is \((8, -2)\)