Question

1. Slove the system of equations, first by graphing, and then algebraically. (8 points) y=x-2 and y=-2x+7

Answer 1

The solution of the equation is $x=3$ and $y=1$

Explanation:

The equations are $y=x-2$ and $y=-2 x+7$

First we shall solve the equation graphically.

The image of the graph is attached below.

This contains the solution to the system of equations.

The equations $y=x-2$ and $y=-2 x+7$ are plotted on the graph.

The intersection of these two equations are the solutions of the system of equations.

Thus, the intersection of the two equations are $x=3$ and $y=1$

Now, we shall solve the equation algebraically.

Let us solve the equation using substitution method.

Let us substitute $y=x-2$ in $y=-2 x+7$, we get,

$x-2=-2x+7$

Adding both sides by 2x, we have,

$3x-2=7$

Adding both sides by 2, we get,

$3x=9$

Dividing both sides by 3,

$x=3$

Thus, the value of x is 3.

Substituting $x=3$ in $y=x-2$, we get,

$y=3-2\\y=1$

Thus, the value of y is 1.

Hence, The solution of the equation is $x=3$ and $y=1$