Sure! To solve this system of equations, follow these steps:
1. Write down the system of equations:
[tex]\[
\begin{cases}
4x + 3y = 20 \\
2x - y = 0
\end{cases}
\][/tex]
2. Solve one of the equations for one variable in terms of the other. Let's solve the second equation for [tex]\( y \)[/tex]:
[tex]\[
2x - y = 0 \implies y = 2x
\][/tex]
3. Substitute this expression for [tex]\( y \)[/tex] in the first equation:
[tex]\[
4x + 3(2x) = 20
\][/tex]
4. Simplify and solve for [tex]\( x \)[/tex]:
[tex]\[
4x + 6x = 20 \\
10x = 20 \implies x = 2
\][/tex]
5. Substitute the value of [tex]\( x \)[/tex] back into the equation [tex]\( y = 2x \)[/tex] to find [tex]\( y \)[/tex]:
[tex]\[
y = 2(2) \implies y = 4
\][/tex]
So, the solution to the system of equations is [tex]\((x, y) = (2, 4)\)[/tex].
To identify the correct graph:
- The x-coordinate of the intersection point should be 2.
- The y-coordinate of the intersection point should be 4.
Look for the graph where the two lines cross at the point (2, 4). This is where both equations are satisfied simultaneously. The graph that displays this intersection point is the correct one.
