Question

A system of equations is graphed on the coordinate plane. y=−x+5y=2x−1 What is the solution to the system of equations? Enter the coordinates of the solution

Answer 1

The solution of this system of equations is (2,3).

Explanation:

We are given the system of equations,

`y=-x+5`

`y=2x-1`

Plotting the equations, we see that,

The point where the graph of these equations intersect is (2,3).

We know,

The intersection point of two equations is represented by the solution of the system of equations.

Thus, we have,

The solution of this system of equations is (2,3).

That is, x= 2 and y= 3.

Answer 2

we have

`y=-x+5` ------> equation A

`y=2x-1` ------> equation B

Method 1

Equate equation A and equation B

`-x+5=2x-1`

solve for x

`2x+x=5+1`

`3x=6`

`x=2`

Find the value of y

`y=2x-1`

`y=2*2-1=3`

The solution is the point
`(2,3)`

therefore

the answer is

`(2,3)`

Method 2

we know that

The intersection point both graphs is the solution of the system of linear equations

using a graphing tool

see the attached figure

the intersection point is
`(2,3)`

therefore

the answer is

`(2,3)`