# Sample quiz on substitution method Main home here.

1. If a linear system $2x-3y=11,~3x+5y=-12$ is first re-written as $10x-15y=55,~9x+15y=-36$, which method of solution is the solver most likely trying to use?
Substitution
Elimination
Graphing
None of the above
2. If, in a linear system $x+2y=7,~3x+5y=18$ one first writes $x=7-2y$, followed by $3(7-2y)+5y=18$, then one is trying to use $\cdots$
Substitution
Elimination
Graphing
None of the above
3. Given $2x-y=7,~x=3+2y$, the correct substitution to make is $\cdots$?
$2x(3+2y)-y=7$
$2(3+2y)+y=7$
$x(3+2y)-y=7$
$2(3+2y)-y=7$
4. Given $x+y=7,~3x+4y=17$, which of the following is true?
$3x+4(x-7)=17$
$3x+4(7-x)=17$
$3x+4y(7-x)=17$
$3x+4y(x-7)=17$
5. Given $x+2y=9,~3x-7y=14$, which of the following results from the substitution method?
$3(9-2y)+7y=14$
$3(2y-9)-7y=14$
$3(9-2y)-7y=14$
$3x(9-2y)-7y=14$
6. Solve by substitution: $2x-y=7,~x=3+2y$
$x=\frac{11}{3},~y=\frac{1}{3}$
$x=\frac{7}{3},~y=\frac{1}{3}$
$x=\frac{17}{5},~y=\frac{1}{5}$
$x=\frac{8}{3},~y=-\frac{1}{3}$
7. Given $3x-y=7,~5x+4y=6$, isolate $y$ from the first equation, then substitute into the second equation
$5x+4(7-3x)=6$
$5x+4(3x+7)=6$
$5x+4(3x-7)=6$
$5x-4(3x-7)=6$
8. Solve by substitution: $x+y=7,~5x+7y=45$
$x=5,y=2$
$x=3,y=4$
$x=1,y=6$
$x=2,y=5$
9. Solve by substitution: $3x+y=8,~5x-2y=6$
$x=2,y=2$
$x=1,y=5$
$x=4,y=7$
$x=2,y=-2$
10. Solve by substitution: $x-y=10,~4x+3y=12$
$x=6,y=4$
$x=6,y=-4$
$x=7,y=-3$
$x=4,y=-6$