Question

Solve the system of equations. 8x−3y= −22 y=10+4

Answer 1

To solve the given system of equations, we need to simplify the second equation and then substitute into the first equation.

1. The second equation is \( y = 10 + 4 \). Simplifying this gives:
\[
y = 14
\]

2. Now, we substitute \( y = 14 \) into the first equation \( 8x - 3y = -22 \):
\[
8x - 3(14) = -22
\]
\[
8x - 42 = -22
\]

3. Next, we add 42 to both sides to isolate the term with \( x \):
\[
8x = -22 + 42
\]
\[
8x = 20
\]

4. Now, divide both sides by 8 to solve for \( x \):
\[
x = \frac{20}{8} = \frac{5}{2} = 2.5
\]

Now we have the solution:
\[
x = 2.5 \quad \text{and} \quad y = 14
\]

Thus, the solution to the system of equations is:
\[
\boxed{\left( \frac{5}{2}, 14 \right)} \quad \text{or} \quad \boxed{(2.5, 14)}
\]