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.
To review the graphs of the system, we can first graph each equation separately and then analyze their intersection.
The graph of the equation y = 4x - 10 is a straight line with a slope of 4 and a y-intercept of -10. It means that if we increase x by 1 unit, y will increase by 4 units, and the line crosses the y-axis at (0, -10).
The graph of the equation y = -2x + 8 is also a straight line, but with a slope of -2 and a y-intercept of 8. If we increase x by 1 unit, y will decrease by 2 units, and the line crosses the y-axis at (0, 8).
Now, let's analyze their intersection. The point at which these two lines intersect is the solution to the system of equations. We can find this point by solving the system algebraically or by visually inspecting the graphs.
By solving the system algebraically, we can equate the expressions for y and solve for x:
4x - 10 = -2x + 8
6x = 18
x = 3
Substituting this value of x into either equation, we can solve for y:
y = 4(3) - 10
y = 12 - 10
y = 2
So, the solution to the system of equations is (3, 2).
Visually inspecting the graphs, we can see that the two lines intersect at the point (3, 2), which confirms our algebraic solution.
In conclusion, the system of equations y = 4x - 10 and y = -2x + 8 has a solution at (3, 2).