5u+2v=-15
3u+v=-8 Im not sure how to do this problem
double the 2nd:
6u + 2v = -16
5u + 2v = -15
subtract them:
u = -1
sub into 2nd:
-3 + v = -8
v = -5
v = -5 and u = -1
(curious why you called this "college math", this is grade 7 )
To solve this system of equations, you can use the method of substitution or the method of elimination. Let's use the method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for v in terms of u:
3u + v = -8
v = -3u - 8
Step 2: Substitute the expression obtained for the variable in the other equation.
Now substitute -3u - 8 for v in the first equation:
5u + 2(-3u - 8) = -15
Step 3: Simplify and solve for u.
5u - 6u - 16 = -15
-u - 16 = -15
-u = 1
u = -1
Step 4: Substitute the value of u back into one of the original equations to solve for v.
Let's use the first equation:
5(-1) + 2v = -15
-5 + 2v = -15
2v = -15 + 5
2v = -10
v = -10/2
v = -5
Step 5: Check your solution by substituting the values of u and v back into both original equations.
For the first equation:
5u + 2v = -15
5(-1) + 2(-5) = -15
-5 - 10 = -15
-15 = -15 (True)
For the second equation:
3u + v = -8
3(-1) + (-5) = -8
-3 - 5 = -8
-8 = -8 (True)
Therefore, the solution to the system of equations is u = -1 and v = -5.