Substitution method:
We can substitute the first equation into the second equation for y, giving us:
4x + x = 5
Simplifying:
5x = 5
x = 1
Now we can use the first equation to solve for y:
y = 4(1)
y = 4
Therefore, the solution to the system of equations is (1,4).
Graphing method:
We can graph each equation on the same coordinate axes and look for the intersection point:
y = 4x
y + x = 5
To graph y = 4x, we can plot the point (0,0) and use the slope of 4 to find additional points. We can also use the x-intercept (where y = 0) to find another point:
y = 4x
0 = 4x
x = 0
So the point (0,0) and (1,4) are on the first line.
To graph y + x = 5, we can rearrange to solve for y and graph the line using two points:
y = 5 - x
When x = 0, y = 5. When x = 5, y = 0. So the points (0,5) and (5,0) are on the second line.
Graphing the two lines, we see that they intersect at the point (1,4). This confirms our solution found using substitution.
*[illustration IMG_0288_(1).JPG]
find the solution the the system of equations by using either graphing or substitution
Y = 4x and y + x = 5
1 answer