1) Solve the system of equations using the substitution method.
2x+8y=4
x=−3y+5
we have that
2(−3y+5)+8y=4---------- > -6y+10+8y=4---------- > 2y=-6-----> y=-3
x=−3y+5----------> x=−3*(-3)+5=14
the answer is
x=14
y=-3
2 Solve the system of equations using the linear combination method.
5m+3n=41---------- > 2*[5m+3n=41]---------------- > 10m+6n=82
3m−6n=9-------------------------------------------------- > 3m−6n=9
---------------------
13m+0n=91
m=91/13=7
3m−6n=9--------------- > 3*7−6n=9----------- >21-9=6n-----------> n=2
the answer is
m=7
n=2
3. Solve the system of equations using the linear combination method.
6g+8h=40
−6g+2h=−20
------------------
0+10h=20------------- > h=2
6g+8h=40--- > 6g+8*2=40-> 6g=24-> g=4
the answer is
h=2
g=4
4. Solve the system of equations using the linear combination method.
9x+5y=35------------- > -1*[9x+5y=35]--------> -9x-5y=-35
2x+5y=0-------------------------------------------- > 2x+5y=0
----------------------
-7x+0=-35
x=5
9x+5y=35- > 9*5+5y=35---- > 5y=-10--------- > y=-2
the answer is
x=5
y=-2