Solve the system by graphing.
2 x minus 5 y
equals
20
4 x minus 10 y
equals
negative 40
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Part 1
Use the graphing tool to graph the system.



To solve this system of equations by graphing, we'll first convert each equation into slope-intercept form (\( y = mx + b \)) and then plot them.

The given system of equations is:

\[
2x - 5y = 20 \quad \text{(Equation 1)}
\]
\[
4x - 10y = -40 \quad \text{(Equation 2)}
\]

### Step 1: Convert each equation to slope-intercept form

**Equation 1: \( 2x - 5y = 20 \)**

- Solve for \( y \):
\[
2x - 5y = 20 \quad \Rightarrow \quad -5y = -2x + 20
\]
\[
y = \frac{2}{5}x - 4
\]

**Equation 2: \( 4x - 10y = -40 \)**

- Solve for \( y \):
\[
4x - 10y = -40 \quad \Rightarrow \quad -10y = -4x - 40
\]
\[
y = \frac{2}{5}x - 4
\]

### Step 2: Graph the equations

Both equations simplify to the same line: \( y = \frac{2}{5}x - 4 \).

### Step 3: Analyze the system

Since both equations represent the same line, they overlap completely. This means that every point on the line is a solution to the system

Solve the system by graphing.
2x - 5y = 20
4x - 10y = -40


Learn how to solve the system of linear equations 2x - 5y = 20 and 4x - 10y = -40 by graphing. This problem involves converting equations to slope-intercept form and analyzing coincident lines. Ideal for students in Grades 8-10.

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