Question

x+y=4
3x+4y=10

Answer 1

To solve the system of equations:

1. \( x + y = 4 \) (Equation 1)
2. \( 3x + 4y = 10 \) (Equation 2)

We can use substitution or elimination. Here, we will use substitution.

From Equation 1, solve for \( y \):

\[
y = 4 - x
\]

Now, substitute this expression for \( y \) into Equation 2:

\[
3x + 4(4 - x) = 10
\]

Distribute the 4:

\[
3x + 16 - 4x = 10
\]

Combine like terms:

\[
-1x + 16 = 10
\]

Subtract 16 from both sides:

\[
-1x = 10 - 16
\]
\[
-1x = -6
\]

Divide by -1:

\[
x = 6
\]

Now substitute \( x \) back into the equation we found for \( y \):

\[
y = 4 - 6 = -2
\]

So the solution to the system of equations is:

\[
x = 6, \quad y = -2
\]

To summarize, the solution is:

\[
(x, y) = (6, -2)
\]