Question: User: 7x + 9y = 119
2x + y = 23
3x^2 - 3 by -2 - x
4\u221a63 - 3\u221a28
2\u221a2(5\u221a10 - 3\u221a2)
4m^2yp + 6/(m^2y)
k^2/(2p) + c - 4/(p^2c)
(0.0007 \u00d7 10^-23)(4000 \u00d7 10^6) / ((0.00004)(7,000,000))
3x + 2y = 12
5x - 4y = 8
(a) is a diagonal line rising from left to right, crossing the y-axis at 2 and the x-axis at -2, so position_hint 60; {center}.
(b) is a horizontal line at y = -4, so position_hint 60; {center}.
706
A, B, C, D
The circle diagram has a 706 arc on the right side between the lower-right point and the rightmost point, with A in the lower-right central sector, B near the center, C on the left interior, and D in the upper-right interior, so position_hint 60; {center}.
\u221a21
\u221a21
4
The isosceles triangle has two equal sides labeled \u221a21 and a base labeled 4, so position_hint 60; {center}.
(-2, 5) and (-6, -3)
(5, -3)
2/9
k
3
4
9
The lower figure shows a large triangle with base 9, a segment parallel to the base labeled 4, and the left side split into an upper segment labeled 3 and a lower segment labeled k, so position_hint 60; {bottom-left}.
1. **Problem:** Solve the system of linear equations:
$$7x + 9y = 119$$
$$2x + y = 23$$
2. **Formula and rules:** To solve a system of linear equations, we can use substitution or elimination. Here, we use substitution.
3. **Step 1:** Solve the second equation for $y$:
$$2x + y = 23 \implies y = 23 - 2x$$
4. **Step 2:** Substitute $y = 23 - 2x$ into the first equation:
$$7x + 9(23 - 2x) = 119$$
5. **Step 3:** Expand and simplify:
$$7x + 207 - 18x = 119$$
$$7x - 18x = 119 - 207$$
$$-11x = -88$$
6. **Step 4:** Divide both sides by $-11$:
$$x = \frac{-88}{-11} = \cancel{\frac{-88}{-11}} = 8$$
7. **Step 5:** Substitute $x = 8$ back into $y = 23 - 2x$:
$$y = 23 - 2(8) = 23 - 16 = 7$$
8. **Answer:** The solution to the system is:
$$x = 8, \quad y = 7$$
This means the lines intersect at the point $(8,7)$.