To solve the given system of equations step-by-step, follow these steps:
1. Write down the given equations:
[tex]\[
\begin{cases}
7x + 10y = 36 \quad \text{(Equation 1)} \\
y = 2x + 9 \quad \text{(Equation 2)}
\end{cases}
\][/tex]
2. Substitute Equation 2 into Equation 1:
Since Equation 2 gives us [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex], we can substitute [tex]\( y = 2x + 9 \)[/tex] into Equation 1:
[tex]\[
7x + 10(2x + 9) = 36
\][/tex]
3. Expand and simplify:
[tex]\[
7x + 20x + 90 = 36
\][/tex]
Combine like terms:
[tex]\[
27x + 90 = 36
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Subtract 90 from both sides:
[tex]\[
27x = 36 - 90
\][/tex]
[tex]\[
27x = -54
\][/tex]
Divide both sides by 27:
[tex]\[
x = -2
\][/tex]
5. Substitute [tex]\( x = -2 \)[/tex] back into Equation 2 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 2(-2) + 9
\][/tex]
Calculate the value:
[tex]\[
y = -4 + 9
\][/tex]
[tex]\[
y = 5
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
x = -2
\][/tex]
[tex]\[
y = 5
\][/tex]
