Question

To solve the system of equations using substitution, we have the two equations:
y=−3x+4
x+13y=43
Step 1: Substitute y from the first equation into the second equation.
We know that y=−3x+4. We can substitute this into the second equation:
x+13(−3x+4)=43
Step 2: Simplify the second equation.
Now, simplifying the left side:
x−3x3+43=43
This simplifies to:
x−x+43=43
Step 3: Simplify further.
This leads us to:
43=43
This is a true statement, which means that any value of x will satisfy this equation due to its equivalence. Therefore, the system of equations has infinitely many solutions.
Step 4: Express the solution set.
To express this solution, we can go back to the first equation y=−3x+4. We can express y in terms of x:
y=−3x+4
Final Answer:
The solution set can be written as:
can you make this way less advanced and use way less words and only give me the solution and how u got it

Answer 1

To solve the system of equations:

1. Start with \( y = -3x + 4 \).
2. Substitute into the second equation:
\[
x + 13(-3x + 4) = 43
\]
3. Simplify:
\[
x - 39x + 52 = 43
\]
which becomes
\[
-38x + 52 = 43
\]
then
\[
-38x = -9
\]
leading to
\[
x = \frac{9}{38}
\].
4. Substitute back to find \( y \):
\[
y = -3\left(\frac{9}{38}\right) + 4 = \frac{114}{38} - \frac{27}{38} = \frac{87}{38}
\]

The solution is:
\[
(x, y) = \left( \frac{9}{38}, \frac{87}{38} \right)
\]