Question

Solve the system of equations 3, x, plus, y, equals, 43x+y=4 and minus, x, plus, 2, y, equals, 15−x+2y=15 by combining the equations.
Below, two sets of the two equations are shown. The first set has input boxes in front of each equation to put a number to multiply it by. When you enter a number, the corresponding equation below changes to be the result of the multiplication. Under the second set, a resulting equation is shown with input boxes for the coefficients and constant. Then, there is a "try" button. When you press the try button, if your answer is correct, it will be placed on the page and a new question will appear with a new input box. This process will continue until the final answer area appears with the submit button.
left parenthesis, 3, x(3x plus, y+y equals= 4, right parenthesis4)
left parenthesis, minus, x(−x plus, 2, y+2y equals= 15, right parenthesis15)
3, x3x plus, y+y equals= 44
minus, x−x plus, 2, y+2y equals= 1515
0
0xx plus+
0
0yy equals=

Answer 1

Let's solve the system of equations step by step.

The equations given are:

1. \( 3x + y = 4 \)
2. \( -x + 2y = 15 \)

We can use the method of elimination or substitution to solve this system. Let's use elimination method:

First, we'll align the equations:

\[
\begin{align*}
1) & \quad 3x + y = 4 \quad \text{(Equation 1)} \\
2) & \quad -x + 2y = 15 \quad \text{(Equation 2)}
\end{align*}
\]

Next, we can multiply Equation 2 by 3 so that the coefficient of \( x \) will match in both equations (making it possible to eliminate \( x \)):

\[
3(-x + 2y) = 3(15)
\]

This gives us:

\[
-3x + 6y = 45 \quad \text{(Equation 3)}
\]

Now we have:

1) \( 3x + y = 4 \)

3) \( -3x + 6y = 45 \)

Now we can add Equation 1 and Equation 3:

\[
(3x + y) + (-3x + 6y) = 4 + 45
\]

This simplifies to:

\[
7y = 49
\]

Now, divide both sides by 7:

\[
y = 7
\]

Now that we have \( y \), we can substitute it back into one of the original equations to find \( x \). Using Equation 1:

\[
3x + 7 = 4
\]

Subtract 7 from both sides:

\[
3x = 4 - 7
\]
\[
3x = -3
\]

Now, divide both sides by 3:

\[
x = -1
\]

Thus, the solution to the system of equations is:

\[
x = -1 \quad \text{and} \quad y = 7
\]

In summary, the final answer is:

\[
\boxed{(-1, 7)}
\]