Question

MEDALS FOR WHO SOLVES THE EQUATIONS!
Substitution by elimination
•7. 2x – 3y = 4 and 3x + 2y = 6
Answer: (2,0)
•8. 2x – 5y = 6 and 4x + 3y = -1
Answer: (1/2,1)
How do you solve to get these answers. Show work

Answer 1

have you cover doing system of equations yet?

Answer 2

yes

Answer 3

\(\large \begin{array}{llll}
2x - 3y = 4&{\color{red}{ \times 2}}\implies &4x\cancel{-6y}=8\\
3x + 2y = 6&{\color{red}{ \times 3}}\implies &9x\cancel{+6y}=18\\
\hline\\
&&\square x\qquad =\square
\end{array}\)

that'd give you "x", then substitute on either equation to get "y"

Answer 4

do you add or subtract.

Answer 5

you add, then again, if the number is negative, the adding will turn to subtraction anyway

Answer 6

okay. So it would be 13x=26

Answer 7

yeap

Answer 8

which means x = 26/13

Answer 9

x=2

Answer 10

then you can grab that "x" and put it on either equation, solve for "y"

Answer 11

2x-3y = 4
2(2)-3y=4 => 4-3y=4

Answer 12

\(\large \begin{array}{llll}
2x - 5y = 6&{\color{red}{ \times -2}}\implies &-4x+10y=-12\\
4x + 3y = -1&&\quad 4x + 3y = -1\\
\hline\\
&&\qquad \quad 13 y=-13
\end{array}\)

Answer 13

and you do the same on that one, once one of the variables has been ELIMINATED, then the rest is just solving for the other

Answer 14

\(\large \begin{array}{llll}
2x - 5y = 6&{\color{red}{ \times -2}}\implies &\cancel{-4x}+10y=-12\\
4x + 3y = -1&&\quad \cancel{4x} + 3y = -1\\
\hline\\
&&\qquad \quad 13 y=-13
\end{array}\\\quad\\
{\color{blue}{ 13}}y=-13\implies y=\cfrac{-13}{{\color{blue}{ 13}}}\implies y=-1\)

Answer 15

how do you get 1/2 for x?

Answer 16

well we dunno what "x" is yet
since we know "y", we'll use that in either equation, say the 2nd one

so \(\bf 4x+3{\color{red}{ y}}=-1\implies 4x+3({\color{red}{ -1}})=-1\implies 4x-3=-1\)

Answer 17

anyhow, that gives an "x", but is not 1/2 though

Answer 18

okay thanks.

Answer 19

yw