Answer:
u=4, v=1, or as a point, (4, 1)
Step-by-step explanation:
Hi there!
We are given the following system:
3u + 3v = 15
-2u + 3v = -5
We are asked to solve this system by elimination, where we will add the two equations together to clear one of the variables, solve for the non-cleared variable, then substitute the value of the non-cleared variable to find the value of the variable that was originally cleared
Because we want to clear one of the variables, we need to make sure that the coefficients in front of the variable we want to clear are opposites; like -2 and 2
3v is in both equations, but it's both positive. So let's multiply one of the equations by -1 to change the sign of it
Taking the second equation for example,
-1(-2u + 3v = -5)
Multiply
2u - 3v = 5
Now stack up the equations again:
3u + 3v = 15
2u - 3v = 5
Add the equations together:
5u=20
Divide both sides by 5
u=4
Now substitute 4 as the value of u into one of the equations to solve for v
Using 3u + 3v =15 for example,
3(4)+3v=15
Multiply
12 + 3v=15
Subtract 12 from both sides
3v=3
Divide both sides by 3
v=1
The answer is u=4, v=1, or as a point, (4, 1)
Hope this helps!
