Question

slove the following equations
2x-3y=8, 3x +5y=10​

Answer 1

EXPLANATION.

⇒ 2x - 3y = 8. - - - - - (1).

⇒ 3x + 5y = 10. - - - - - (2).

Multiply equation (1) by 5.

Multiply equation (2) by 3.

⇒ 2x - 3y = 8. - - - - - (1).   x  5.

⇒ 3x + 5y = 10. - - - - - (2).   x  3.

We get.

⇒ 10x - 15y = 40. - - - - - (3).

⇒ 9x + 15y = 30. - - - - - (4).

Adding equation (3) and equation (4), we get.

⇒ 10x + 9x = 40 + 30.

⇒ 19x = 70.

⇒ x = 70/19.

Put the value of x = 70/19 in equation (2), we get.

⇒ 3x + 5y = 10. - - - - - (2).

⇒ 3(70/19) + 5y = 10.

⇒ 210/19 + 5y = 10.

⇒ 5y = 10 - (210/19).

⇒ 5y = (190 - 210)/(19).

⇒ 5y = - 20/19.

⇒ y = - 4/19.

∴ value of x is 70/19  and  y is - 4/19.

Answer 2

Step-by-step explanation:

Solve for x.

$\sf \leadsto 2x-3y=8 \\ \\\leadsto \sf2x=8+3y \\ \\ \sf \leadsto x=\frac{8+3y}{2} \:$

Substitute x=8+3y/2 into 3x+5y=10

Starting with the original equation.

$\sf \: 3x+5y=10$

Let $\sf \: x=\frac{8+3y}{2}$

$\sf \leadsto3\times \frac{8+3y}{2}+5y=10 \\ \\ \sf \leadsto\frac{3(8+3y)}{2}+5y=10 \:$

Solve for y.

$\sf \leadsto\frac{3(8+3y)}{2}+5y=10 \: \\ \\ \sf \leadsto3(8+3y)+10y=20 \\ \\ \sf\leadsto24+9y+10y=20 \: \: \: \\ \\ \sf\leadsto 24+19y=20 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\leadsto 19y=20−24 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\leadsto19y=−4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \leadsto \: y = \frac{ - 4}{19} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Substitute $\sf \: y=-\frac{4}{19}$into $\sf \: x=\frac{8+3y}{2}$

Starting with the original equation.

$\sf \leadsto x=\frac{8+3y}{2}$

Let $\sf \: y=-\frac{4}{19}$

$\sf \leadsto x=\frac{8+3\times \frac{-4}{19}}{2} \\ \\ \sf \leadsto x = \frac{70}{19} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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Therefore,

$\begin{aligned}& \bf \: x=\frac{70}{19}\\ \\ & \bf \: y=-\frac{4}{19}\end{aligned}$