Question

How to solve this system of equation and the solution

Answer 1

Solution

Step 1:

Define the variables:

s = sugar cookie dough

g = gingerbread cookie dough

Step 2:

Write systems of equations.

s = cost sugar cookie dough

g = cost gingerbread cookie dough

$\begin{gathered} 8s\text{ + 5g = }179 \\ 1s\text{ + }6g\text{ = 103} \end{gathered}$

Solve

Use the substitution method to substitute s from the second equation into the first equation.

$\begin{gathered} \text{s = 103 - 6g} \\ \text{substitute s = 103 - 6g in the second equation.} \\ 8(103\text{ - }6g)\text{ + 5g = 179} \\ 824\text{ - 48g + 5g = 179} \\ 824\text{ - 179 = 48g - 5g} \\ 645\text{ = 43g} \\ g\text{ = }\frac{645}{43} \\ g\text{ = 15} \end{gathered}$

Next, find the value of s.

$\begin{gathered} \text{s = 103 - 6}\times15 \\ s\text{ = 103 - 90} \\ s\text{ = 13} \end{gathered}$

Write the solution as a complete sentence below:

One package of sugar cookie dough cost = $13

One package of gingerbread cookie dough cost = $15