Løs sqrt{37}(10x+7y+5)=sqrt{149}(6x-y-23)

$$\sqrt { 37 } ( 10 x + 7 y + 5 ) = \sqrt { 149 } ( 6 x - y - 23 )$$

Løs for x

$$x=\frac{\sqrt{5513}y+67y+5\sqrt{5513}+431}{32}$$

Vejledning i at løse lineær ligning

Brug fordelingsegenskaben til at multiplicere \sqrt{37} med 10x+7y+5.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}=\sqrt{149}\left(6x-y-23\right)$$

Brug fordelingsegenskaben til at multiplicere \sqrt{149} med 6x-y-23.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}=6\sqrt{149}x-\sqrt{149}y-23\sqrt{149}$$

Subtraher 6\sqrt{149}x fra begge sider.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}-6\sqrt{149}x=-\sqrt{149}y-23\sqrt{149}$$

Subtraher 7\sqrt{37}y fra begge sider.

$$10\sqrt{37}x+5\sqrt{37}-6\sqrt{149}x=-\sqrt{149}y-23\sqrt{149}-7\sqrt{37}y$$

Subtraher 5\sqrt{37} fra begge sider.

$$10\sqrt{37}x-6\sqrt{149}x=-\sqrt{149}y-23\sqrt{149}-7\sqrt{37}y-5\sqrt{37}$$

Kombiner alle led med x.

$$\left(10\sqrt{37}-6\sqrt{149}\right)x=-\sqrt{149}y-23\sqrt{149}-7\sqrt{37}y-5\sqrt{37}$$

Ligningen er nu i standardform.

$$\left(10\sqrt{37}-6\sqrt{149}\right)x=-7\sqrt{37}y-\sqrt{149}y-5\sqrt{37}-23\sqrt{149}$$

Divider begge sider med 10\sqrt{37}-6\sqrt{149}.

$$\frac{\left(10\sqrt{37}-6\sqrt{149}\right)x}{10\sqrt{37}-6\sqrt{149}}=\frac{-7\sqrt{37}y-\sqrt{149}y-5\sqrt{37}-23\sqrt{149}}{10\sqrt{37}-6\sqrt{149}}$$

Division med 10\sqrt{37}-6\sqrt{149} annullerer multiplikationen med 10\sqrt{37}-6\sqrt{149}.

$$x=\frac{-7\sqrt{37}y-\sqrt{149}y-5\sqrt{37}-23\sqrt{149}}{10\sqrt{37}-6\sqrt{149}}$$

Divider -\sqrt{149}y-23\sqrt{149}-7\sqrt{37}y-5\sqrt{37} med 10\sqrt{37}-6\sqrt{149}.

$$x=\frac{\frac{3\sqrt{149}+5\sqrt{37}}{416}\left(7\sqrt{37}y+\sqrt{149}y+5\sqrt{37}+23\sqrt{149}\right)}{2}$$

Løs for y

$$y=\frac{\sqrt{5513}x-67x+41-3\sqrt{5513}}{32}$$

Vejledning i at løse lineær ligning

Brug fordelingsegenskaben til at multiplicere \sqrt{37} med 10x+7y+5.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}=\sqrt{149}\left(6x-y-23\right)$$

Brug fordelingsegenskaben til at multiplicere \sqrt{149} med 6x-y-23.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}=6\sqrt{149}x-\sqrt{149}y-23\sqrt{149}$$

Tilføj \sqrt{149}y på begge sider.

$$10\sqrt{37}x+7\sqrt{37}y+5\sqrt{37}+\sqrt{149}y=6\sqrt{149}x-23\sqrt{149}$$

Subtraher 10\sqrt{37}x fra begge sider.

$$7\sqrt{37}y+5\sqrt{37}+\sqrt{149}y=6\sqrt{149}x-23\sqrt{149}-10\sqrt{37}x$$

Subtraher 5\sqrt{37} fra begge sider.

$$7\sqrt{37}y+\sqrt{149}y=6\sqrt{149}x-23\sqrt{149}-10\sqrt{37}x-5\sqrt{37}$$

Kombiner alle led med y.

$$\left(7\sqrt{37}+\sqrt{149}\right)y=6\sqrt{149}x-23\sqrt{149}-10\sqrt{37}x-5\sqrt{37}$$

Ligningen er nu i standardform.

$$\left(\sqrt{149}+7\sqrt{37}\right)y=6\sqrt{149}x-10\sqrt{37}x-5\sqrt{37}-23\sqrt{149}$$

Divider begge sider med 7\sqrt{37}+\sqrt{149}.

$$\frac{\left(\sqrt{149}+7\sqrt{37}\right)y}{\sqrt{149}+7\sqrt{37}}=\frac{6\sqrt{149}x-10\sqrt{37}x-5\sqrt{37}-23\sqrt{149}}{\sqrt{149}+7\sqrt{37}}$$

Division med 7\sqrt{37}+\sqrt{149} annullerer multiplikationen med 7\sqrt{37}+\sqrt{149}.

$$y=\frac{6\sqrt{149}x-10\sqrt{37}x-5\sqrt{37}-23\sqrt{149}}{\sqrt{149}+7\sqrt{37}}$$

Divider 6\sqrt{149}x-23\sqrt{149}-10\sqrt{37}x-5\sqrt{37} med 7\sqrt{37}+\sqrt{149}.

$$y=\frac{\sqrt{5513}x-67x+41-3\sqrt{5513}}{32}$$