Question: Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
{
y = -2x + 7
y = 5x - 7
}
x =
y =
1. **State the problem:** We need to find the solution to the system of equations:
$$y = -2x + 7$$
$$y = 5x - 7$$
2. **Set the equations equal to each other:** Since both expressions equal $y$, we can set them equal:
$$-2x + 7 = 5x - 7$$
3. **Solve for $x$:**
Add $2x$ to both sides:
$$\cancel{-2x} + 7 + 2x = 5x - 7 + 2x$$
$$7 = 7x - 7$$
Add $7$ to both sides:
$$7 + 7 = 7x - 7 + 7$$
$$14 = 7x$$
Divide both sides by $7$:
$$\frac{14}{\cancel{7}} = \frac{7x}{\cancel{7}}$$
$$2 = x$$
4. **Find $y$ by substituting $x=2$ into one of the original equations:**
Using $$y = -2x + 7$$:
$$y = -2(2) + 7 = -4 + 7 = 3$$
5. **Final solution:**
$$x = 2, \quad y = 3$$
This means the two lines intersect at the point $(2, 3)$.