How do you find the solution of the system of equations $x + 2 y = 5$ $x+2y=5$ and $2 x - 3 y = - 4$ $2x-3y=-4$ ?

Question

How do you find the solution of the system of equations $x + 2 y = 5$ $x+2y=5$ and $2 x - 3 y = - 4$ $2x-3y=-4$ ?

1 Answer

Impact of this question

2297 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-21T08:46:12

The answer is $x = 5 - 2 y$ $x=5-2y$ and $y = 2$ $y=2$

Problem: Solve the system of equations $x + 2 y = 5$ $x+2y=5$ and $2 x - 3 y = - 4$ $2x-3y=-4$ .

First equation. Solve for $x$ $x$ .

$x + 2 y = 5$ $x+2y=5$

Subtract $2 y$ $2y$ from both sides.

$x = 5 - 2 y$ $x=5-2y$

Second equation. Solve for $y$ $y$ .

Substitute $5 - 2 y$ $5-2y$ for $x$ $x$ in the other equation. Solve for $y$ $y$ .

$2 x - 3 y = - 4$ $2x-3y=-4$ =

$2 (5 - 2 y) - 3 y = - 4$ $2(5-2y)-3y=-4$

Distribute the $2$ $2$ .

$10 - 4 y - 3 y = - 4$ $10-4y-3y=-4$

Combine like terms.

$- 7 y + 10 = - 4$ $-7y+10=-4$ =

$- 7 y = - 14$ $-7y=-14$

Divide both sides by $- 7$ $-7$ .

$y = 2$ $y=2$

Check your answers by substituting the values for $x$ $x$ and $y$ $y$ back into both of the original equations.

$x + 2 y = 5$ $x+2y=5$ =

$5 - 2 \cdot 2 + 2 \cdot 2 = 5$ $5-2*2+2*2=5$ =

$5 - 4 + 4 = 5$ $5-4+4=5$ =

$5 = 5$ $5=5$

$2 x - 3 y = - 4$ $2x-3y=-4$ =

$2 (5 - 2 \cdot 2) - 3 \cdot 2 = - 4$ $2(5-2*2)-3*2=-4$

Distribute the $2$ $2$ .

$10 - 8 - 6 = - 4$ $10-8-6=-4$ =

$- 4 = - 4$ $-4=-4$

The answers check!

Science

Math

Humanities

... and beyond

How do you find the solution of the system of equations $x + 2 y = 5$ $x+2y=5$ and $2 x - 3 y = - 4$ $2x-3y=-4$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the solution of the system of equations x+2y=5x+2y=5 and 2x−3y=−42x-3y=-4?

1 Answer

Related questions

Impact of this question

How do you find the solution of the system of equations $x + 2 y = 5$ $x+2y=5$ and $2 x - 3 y = - 4$ $2x-3y=-4$ ?