Answer to Question #350623 in Algebra for chris

Question

2x + y = 15

x - y = 9

Answer 1

There are three ways to solve systems of linear equations in two variables:

graphing.

substitution method.

elimination method.

1.

$$2x + y = 15$$ $$x - y = 9$$

a.

$(8, -1)$

b.

$$2x + y = 15$$ $$x - y = 9$$

$$2x + x-9 = 15$$ $$y = x-9$$

$$3x = 24$$ $$y= x-9$$

$$x=8$$ $$y=-1$$

$(8, -1)$

c.

$$2x + y = 15$$ $$x - y = 9$$

$$3x - 2y = 12$$ $$2x + 5y = 72$$

$$2x + y+x-y= 15+9$$ $$x-y=9$$

$$3x = 24$$ $$x-y=9$$

$$x=8$$ $$8-y=9$$ $$x=8$$ $$y=-1$$

$(8, -1)$

2.

$$3x - 2y = 12$$ $$2x + 5y = 72$$

a.

$(\dfrac{204}{19}, \dfrac{192}{19})$

b.

$$3x - 2y = 12$$ $$2x + 5y = 72$$

$$y = \dfrac{3}{2}x-6$$ $$2x+5(\dfrac{3}{2}x-6)=72$$

$$y = \dfrac{3}{2}x-6$$ $$\dfrac{19}{2}x=102$$

$$x=\dfrac{204}{19}$$ $$y=\dfrac{3}{2}(\dfrac{204}{19})-6$$ $$x=\dfrac{204}{19}$$ $$y=\dfrac{192}{19}$$

$(\dfrac{204}{19}, \dfrac{192}{19})$

c.

$$3x - 2y = 12$$ $$2x + 5y = 72$$

$$6x - 4y = 24$$ $$6x + 15y = 216$$

$$6x+15y-(6x-4y)=216-24$$ $$3x-2y=12$$

$$19y=192$$ $$x=\dfrac{2}{3}y+4$$

$$x=\dfrac{204}{19}$$ $$y=\dfrac{192}{19}$$

$(\dfrac{204}{19}, \dfrac{192}{19})$

3.

$$3x - 2y = 12$$ $$2x + 5y = 7$$

a.

$(\dfrac{74}{19}, -\dfrac{3}{19})$

b.

$$3x - 2y = 12$$ $$2x + 5y = 7$$

$$y = \dfrac{3}{2}x-6$$ $$2x+5(\dfrac{3}{2}x-6)=7$$

$$y = \dfrac{3}{2}x-6$$ $$\dfrac{19}{2}x=37$$

$$x=\dfrac{74}{19}$$ $$y=\dfrac{3}{2}(\dfrac{74}{19})-6$$ $$x=\dfrac{74}{19}$$ $$y=-\dfrac{3}{19}$$

$(\dfrac{74}{19}, -\dfrac{3}{19})$

c.

$$3x - 2y = 12$$ $$2x + 5y = 7$$

$$6x - 4y = 24$$ $$6x + 15y = 21$$

$$6x+15y-(6x-4y)=21-24$$ $$3x-2y=12$$

$$19y=-3$$ $$x=\dfrac{2}{3}y+4$$

$$x=\dfrac{74}{19}$$ $$y=-\dfrac{3}{19}$$

$(\dfrac{74}{19}, -\dfrac{3}{19})$