Solve & Substitute Practice AK

Solve the following systems of equations with substitution:

1.

$\eqalign{2x&=4y\\x&=2y\\\text{Substitute}\\3(2y)+5&=y\\6x+5&=y\\5&=-5y\\y&=-1\\x&=-2}$

2.

$\eqalign{x&=2y\\\text{Substitute}\\-3(2y)+8y&=12\\-6y+8y&=12\\2y&=12\\y&=6\\x&=12}$

3.

$\eqalign{-x+1&=3y\\-x&=3y-1\\x&=-3y+1\\\text{Substitute}\\5(-3y+1)-7&=10y\\-15y+5-7&=10y\\-2&=25y\\y&=-\dfrac{2}{25}\\x&=1\dfrac{6}{25}}$

4.

$\eqalign{x-2&=2y\\x&=2y+2\\\text{Substitute}\\20(2y+2)-18&=2y\\40y+40-18&=2y\\22&=-38y\\y&=-\dfrac{22}{38}=-\dfrac{11}{19}\\x&=\dfrac{16}{19}}$

5.

$\eqalign{-2x&=y-8\\y&=8-2x\\\text{Substitute}\\-x+15(8-2x)&=19\\-x+120-30x&=19\\-31x&=-101\\x&=\dfrac{101}{31}\\y&=1\dfrac{15}{31}}$

6.

$\eqalign{.5x&=4y\\x&=8y\\\text{Substitute}\\2(8y)+2y&=2\\16y+2y&=2\\18y&=2\\y&=\dfrac{1}{9}\\x&=\dfrac{8}{9}}$

7.

$\eqalign{\dfrac{1}{2}x&=6y\\x&=12y\\\text{Substitute}\\2y-5(12y)+5&=15\\2y-60y&=10\\-58y&=10\\y&=\dfrac{10}{58}=\dfrac{5}{29}\\x&=2\dfrac{2}{29}}$

8.

$\eqalign{5x-3&=3y+7\\5x&=3y+10\\x&=\dfrac{3}{5}y+2\\\text{Substitute}\\2(\frac{3}{5}y+2)-11&=y+19\\\dfrac{6}{5}y+4-11&=y+19\\\dfrac{6}{5}y-7&=y+19\\\dfrac{1}{5}y&=26\\y&=130\\x&=78}$

9.

$\eqalign{21x&=7y\\y&=3x\\\text{Substitute}\\15x+15(3x)&=29\\15x+45x&=29\\60x&=29\\x&=\dfrac{29}{60}\\y&=1\dfrac{9}{20}}$

10.

$\eqalign{-x&=-8y\\x&=8y\\\text{Substitute}\\-5(8y)+9&=9y\\-40y+9&=9y\\9&=49y\\y&=\dfrac{9}{49}\\x&=1\dfrac{23}{49}}$