Question

Solve the system by graphing :y=2x-3y=-x+9

Answer 1

(4,5)

Step-by-step explanation:

Given the system of equations:

`\begin{gathered} y=2x-3 \\ y=-x+9 \end{gathered}`

We graph each of the equation using the x and y-intercepts.

First Equation(y=2x-3)

When x=0

`\begin{gathered} y=2x-3 \\ y=2(0)-3 \\ y=-3 \\ \implies(0,-3) \end{gathered}`

When y=0

`\begin{gathered} 0=2x-3 \\ 2x=3 \\ x=(3)/(2) \\ x=1.5 \\ \implies(1.5,0) \end{gathered}`

Next, join the points (0,-3) and (1.5,0) as shown below:

Second Equation(y=-x+9)

When x=0

`\begin{gathered} y=-x+9 \\ y=-0+9 \\ y=9 \\ \implies(0,9) \end{gathered}`

When y=0

`\begin{gathered} 0=-x+9 \\ x=9 \\ \implies(9,0) \end{gathered}`

Next, join the points (0,9) and (9,0) on the same graph as shown below:

The point where the two lines intersect is the solution to the system of equations.

Therefore, the solution is (4,5).