Question

Review the graphs of a system of these two linear equations in two variables: y=4x−10 and y=−2x+8 Find the solution of the system.

Answer 1

To review the graphs of the system of linear equations, let's start by finding the x-intercept and y-intercept of each equation:

For the equation y = 4x - 10, we set y = 0 to find the x-intercept:
0 = 4x - 10
4x = 10
x = 10/4 = 2.5
So, the x-intercept is (2.5, 0).

Next, we set x = 0 to find the y-intercept:
y = 4(0) - 10
y = -10
So, the y-intercept is (0, -10).

For the equation y = -2x + 8, we set y = 0 to find the x-intercept:
0 = -2x + 8
2x = 8
x = 8/2 = 4
So, the x-intercept is (4, 0).

Next, we set x = 0 to find the y-intercept:
y = -2(0) + 8
y = 8
So, the y-intercept is (0, 8).

Now, let's plot these points and draw the lines on a graph:

Graph of y = 4x - 10:
-10 | o
-8
-6 | o
-4
-2 | o
0 | o
2
4 | o
6
8
10

Graph of y = -2x + 8:
10 | o
8 | o
6 | o
4 | o
2
0 | o
-2 | o
-4 | o
-6 | o
-8
-10

Now, let's solve the system of equations to find the solution. The system is given by:

y = 4x - 10
y = -2x + 8

Setting the right-hand sides of the equations equal, we get:

4x - 10 = -2x + 8

Adding 2x to both sides and adding 10 to both sides:

6x = 18

Dividing both sides by 6:

x = 18/6 = 3

Now, substituting this value of x into either of the original equations, we find:

y = 4(3) - 10
y = 12 - 10
y = 2

So, the solution of the system is x = 3 and y = 2.