Question

To solve the system of equations:
Start with y=−3x+4.


Substitute into the second equation:x+13(−3x+4)=43
Simplify:x−39x+52=43which becomes−38x+52=43then−38x=−9leading to x=9/38.
Substitute back to find y:y=−3(9/38)+4=114/38−27/38=87/38
The solution is:(x,y)=(9/38,87/38)
an you make this less advanced and not use fractions

Answer 1

Sure! Let's take it step by step and avoid fractions as much as possible.

We start with the first equation:

1. **Equation 1**: \( y = -3x + 4 \)

Next, we want to use this equation to help us solve the second equation. The second equation is:

2. **Equation 2**: \( x + 13y = 43 \)

Now we will substitute \( y \) from Equation 1 into Equation 2. First, plug \( y = -3x + 4 \) into Equation 2:

\[
x + 13(-3x + 4) = 43
\]

Now, let's distribute \( 13 \):

\[
x - 39x + 52 = 43
\]

Combine like terms:

\[
-38x + 52 = 43
\]

Next, we want to get \( x \) by itself. First, subtract \( 52 \) from both sides:

\[
-38x = 43 - 52
\]

Calculating the right side gives:

\[
-38x = -9
\]

Now, divide both sides by \( -38 \):

\[
x = \frac{9}{38}
\]

Now that we have \( x \), we can find \( y \). Substitute \( x \) back into Equation 1:

\[
y = -3\left(\frac{9}{38}\right) + 4
\]

Calculating this:

\[
y = -\frac{27}{38} + 4
\]

Convert \( 4 \) into a fraction with a denominator of \( 38 \):

\[
4 = \frac{152}{38}
\]

So now, combine:

\[
y = -\frac{27}{38} + \frac{152}{38} = \frac{125}{38}
\]

Thus, the solution to the system of equations is:

\[
(x, y) = \left(\frac{9}{38}, \frac{125}{38}\right)
\]

To avoid fractions altogether, let's multiply both equations by \( 38 \) to eliminate them:

1. Multiply Equation 1: \( 38y = -114x + 152 \)
2. Multiply Equation 2: \( 38x + 494y = 1634 \)

After simplifying, we can solve the new system without dealing with fractions.

Hope this makes it clearer!