Solve the system of equations. 3x - 4y = 40

Question

5x - 5y = 55

Answer 1

To solve the system of equations:

1. $3x-4y=40$ (Equation 1)
2. $5x-5y=55$ (Equation 2)

First, we can simplify Equation 2. Dividing every term by 5 gives us:

$$\begin{array}{}\text{(Equation 2 simplified)}& x-y=11\end{array}$$

Next, we can express $x$ in terms of $y$ from Equation 2:

$$\begin{array}{}\text{(Equation 3)}& x=y+11\end{array}$$

Now, we can substitute Equation 3 into Equation 1:

$$3(y+11)-4y=40$$

Expanding this gives:

$$3y+33-4y=40$$

Combining like terms:

$$-y+33=40$$

To isolate $y$, we can subtract 33 from both sides:

$$-y=40-33$$

$$-y=7$$

Multiplying by -1 gives:

$$y=-7$$

Now, we can substitute $y=-7$ back into Equation 3 to find $x$:

$$x=-7+11$$

$$x=4$$

Now we have the solution:

$$x=4,y=-7$$

To verify, we can substitute these values into the original equations:

1. For Equation 1: $$3(4)-4(-7)=12+28=40\text{(True)}$$

2. For Equation 2: $$5(4)-5(-7)=20+35=55\text{(True)}$$

Thus, the solution to the system of equations is:

$$\boxed{{\displaystyle (4,-7)}}$$