Kathleen Rausch

2021-12-29

Solve the following system of equations algebraically, and check:
$x+2y=4$
$y=2x+7$
Answer: $x=?,y=?$

Robert Pina

Algebraically resolve the system of equations
$x+2y=4$ (1)
$y=2x+7$ (2)
By substitution method, substitute (2) in (1), we get
$x+2\left(2x+7\right)=4$
$⇒x+4x+14=4$
$⇒5x=4-14=-10$
$⇒x=\frac{-10}{5}=-2$
From (2), we set $y=2\left(-2\right)+7$
$y=-4+7=3$
As a result, the answer is:

Putting $x=-2,y=3$ in (1) and (2) were
$-2+2\left(3\right)=1$
$⇒4=4$, which is true
and $3=2\left(-2\right)+7$
$⇒3=-4+7$
$3=3$, which is true.

Paul Mitchell

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:
$2\left(2y+4\right)-y=7$
$4y+8-y=7$
$3y+8=7$
$3y=-1$
$y=-\frac{1}{3}$
Then, plug y back into the first equation to find x.
$x-2\left(-\frac{1}{3}\right)=4$
$x+\frac{2}{3}=4$
$x=\frac{10}{3}$

karton

Put the system of linear equations into standard form:
x+2y=4
2x-y=-7
Solution:
x =-2
y = 3
system matrix
$\left[\begin{array}{cc}1& 2\\ 2& -1\end{array}\right]$
inverse of system matrix
$\left[\begin{array}{cc}0.2& 0.4\\ 0.4& -0.2\end{array}\right]$
determinant of system matrix =-5
graph:
$y=-\left(\frac{1}{2}\right)x+2$
$y=2x+7$

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