Kathleen Rausch

2021-12-29

Solve the following system of equations algebraically, and check:

$x+2y=4$

$y=2x+7$

Answer:$x=?,y=?$

Answer:

Robert Pina

Beginner2021-12-30Added 42 answers

Algebraically resolve the system of equations

$x+2y=4$ (1)

$y=2x+7$ (2)

By substitution method, substitute (2) in (1), we get

$x+2(2x+7)=4$

$\Rightarrow x+4x+14=4$

$\Rightarrow 5x=4-14=-10$

$\Rightarrow x=\frac{-10}{5}=-2$

From (2), we set $y=2(-2)+7$

$y=-4+7=3$

As a result, the answer is:

$x=-2\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}y=3$

Putting $x=-2,y=3$ in (1) and (2) were

$-2+2\left(3\right)=1$

$\Rightarrow 4=4$, which is true

and $3=2(-2)+7$

$\Rightarrow 3=-4+7$

$3=3$, which is true.

Paul Mitchell

Beginner2021-12-31Added 40 answers

Explanation:

First, define one variable (let's do x) in terms of the other (y). Using the first equation, we can conclude that$x=2y+4$ . Then, we can substitute $2y+4$ into anywhere we see x in the second equation, so:

$2(2y+4)-y=7$

$4y+8-y=7$

$3y+8=7$

$3y=-1$

$y=-\frac{1}{3}$

Then, plug y back into the first equation to find x.

$x-2(-\frac{1}{3})=4$

$x+\frac{2}{3}=4$

$x=\frac{10}{3}$

First, define one variable (let's do x) in terms of the other (y). Using the first equation, we can conclude that

Then, plug y back into the first equation to find x.

karton

Expert2022-01-04Added 613 answers

Put the system of linear equations into standard form:

x+2y=4

2x-y=-7

Solution:

x =-2

y = 3

system matrix

inverse of system matrix

determinant of system matrix =-5

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