Question

solve the system of equations by the substitution method.
$y = \frac{5}{8}x+\frac{5}{8}$
$y = \frac{4}{7}x+1$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}. (type an ordered pair.)
b. there are infinitely many solutions.
c. there is no solution.

Explanation:

Step1: Set equations equal

Since $y = \frac{5}{8}x + \frac{5}{8}$ and $y = \frac{4}{7}x + 1$, substitute:
$$\frac{5}{8}x + \frac{5}{8} = \frac{4}{7}x + 1$$

Step2: Eliminate denominators

Multiply all terms by 56 (LCM of 8,7):
$$56\times\frac{5}{8}x + 56\times\frac{5}{8} = 56\times\frac{4}{7}x + 56\times1$$
$$35x + 35 = 32x + 56$$

Step3: Isolate x terms

Subtract $32x$ from both sides:
$$35x - 32x + 35 = 56$$
$$3x + 35 = 56$$

Step4: Solve for x

Subtract 35, then divide by 3:
$$3x = 56 - 35$$
$$3x = 21$$
$$x = 7$$

Step5: Find y value

Substitute $x=7$ into $y = \frac{4}{7}x + 1$:
$$y = \frac{4}{7}\times7 + 1$$
$$y = 4 + 1 = 5$$

Answer:

A. The solution set is $\{(7, 5)\}$. (Type an ordered pair.)