Solve 60x + y = 700; 9 * 5y + z = 1000; 20.8z + 13x = 1170 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$60x+y=700; 9\cdot5y+z=1000; 20.8z+13x=1170$$

Solve for x, y, z

$x = \frac{48890}{4321} = 11\frac{1359}{4321} \approx 11.31451053$
$y = \frac{91300}{4321} = 21\frac{559}{4321} \approx 21.129368202$
$z = \frac{212500}{4321} = 49\frac{771}{4321} \approx 49.178430919$

Short Steps Using Substitution

Solve $60x+y=700$ for $y$.

$$y=700-60x$$

Substitute $700-60x$ for $y$ in the equation $9\times 5y+z=1000$.

$$9\times 5\left(700-60x\right)+z=1000$$

Solve the second equation for $x$ and the third equation for $z$.

$$x=\frac{305}{27}+\frac{1}{2700}z$$ $$z=\frac{225}{4}-\frac{5}{8}x$$

Substitute $\frac{305}{27}+\frac{1}{2700}z$ for $x$ in the equation $z=\frac{225}{4}-\frac{5}{8}x$.

$$z=\frac{225}{4}-\frac{5}{8}\left(\frac{305}{27}+\frac{1}{2700}z\right)$$

Solve $z=\frac{225}{4}-\frac{5}{8}\left(\frac{305}{27}+\frac{1}{2700}z\right)$ for $z$.

$$z=\frac{212500}{4321}$$

Substitute $\frac{212500}{4321}$ for $z$ in the equation $x=\frac{305}{27}+\frac{1}{2700}z$.

$$x=\frac{305}{27}+\frac{1}{2700}\times \frac{212500}{4321}$$

Calculate $x$ from $x=\frac{305}{27}+\frac{1}{2700}\times \frac{212500}{4321}$.

$$x=\frac{48890}{4321}$$

Substitute $\frac{48890}{4321}$ for $x$ in the equation $y=700-60x$.

$$y=700-60\times \frac{48890}{4321}$$

Calculate $y$ from $y=700-60\times \frac{48890}{4321}$.

$$y=\frac{91300}{4321}$$

The system is now solved.

$$x=\frac{48890}{4321}$$ $$y=\frac{91300}{4321}$$ $$z=\frac{212500}{4321}$$