Question

I can not put pictures of the other answer, the points that go with each answer are A. (3,-2)B. (-2,3)C. (1,3)D. (3,1)How do you solve this?

Answer 1

The coordinates of the solution to this system of two linear equations in two variables are: C. (1, 3).

In order to graphically determine the solution for this system of linear equations on a coordinate plane, we would make use of an online graphing calculator to plot the given system of linear equations while taking note of the point of intersection;

y = 2x + 1 ......equation 1.

y = -x + 4 ......equation 2.

Based on the graph shown, we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph that represents them in quadrant I. Hence, this is represented by the ordered pair (1, 3).

In this context, the pair of linear equation has exactly one solution;

x = 1

y = 3

Answer 2

Given

`\begin{gathered} y=2x+1\ldots\text{Equation(i)} \\ y=-x+4\ldots Equation\text{ (i}i) \end{gathered}`

Using Substitution method

Substitute for y in equation(i)

`\begin{gathered} 2x+1=-x+4 \\ \text{collect the like terms} \\ 2x+x=4-1 \\ 3x=3 \\ \text{Divide both sides by 3} \\ (3x)/(3)=(3)/(3) \\ x=1 \end{gathered}`

To get the value of y replace x with 1 in equation (i) or (ii)

`\begin{gathered} y=-x+4\ldots\text{Equation(i}i) \\ y=-1+4 \\ y=3 \end{gathered}`

The final answer

(1,3)

Alternatively Graphically