What is the y-value of the solution to the system of equations?

Question

3x + 5y = 1

7x + 4y = −13

−3
−1
2

Answer 1

To solve the system of equations:

1. 3x + 5y = 1 (Equation 1)
2. 7x + 4y = -13 (Equation 2)

We can use the method of substitution or elimination. Here, I will use substitution.

First, let's solve Equation 1 for $y$:

$$5y=1-3x$$ $$y=\frac{1-3x}{5}$$

Now we substitute this expression for $y$ into Equation 2:

$$7x+4\left(\frac{1-3x}{5}\right)=-13$$

Multiply through by 5 to eliminate the fraction:

$$35x+4(1-3x)=-65$$ $$35x+4-12x=-65$$ $$23x+4=-65$$ $$23x=-65-4$$ $$23x=-69$$ $$x=-3$$

Now we'll substitute $x=-3$ back into the equation we derived for $y$:

$$y=\frac{1-3(-3)}{5}$$ $$y=\frac{1+9}{5}$$ $$y=\frac{10}{5}=2$$

Thus, the y-value of the solution to the system of equations is:

$$\boxed{{\displaystyle 2}}$$