Question

What is the solution to this system of equations? 4x + 5y = 7 3x – 2y = –12What is the solution to this system of equations? 4x + 5y = 7 3x – 2y = –12

Answer 1

The solution of the system of equations is $x=-2$ and $y=3$

Explanation:

The system of equations are $4 x+5 y=7$ and $3 x-2 y=-12$

To determine the solution of the equation, let us solve the equations by elimination method.

Thus, multiplying the equation $4 x+5 y=7$ by 2, we get, $8x+10y=14$

Multiplying the equation $3 x-2 y=-12$ by 5, we get, $15x-10y=-60$

Adding these two equations, we have,

$\ \ 8x+10y=14\\15x-10y=-60\\---------\\23x=-46$

Dividing both sides by 23, we have,

$\frac{23x}{23} =\frac{46}{23}$

  $x=-2$

Thus, the value of x is $x=-2$

Substituting $x=-2$ in the equation $4 x+5 y=7$, we get,

$4 (-2)+5 y=7$

    $-8+5 y=7$

             $5y=15$

               $y=3$

Thus, the value of y is $y=3$

Hence, the solution of the system of equations is $x=-2$ and $y=3$

Answer 2

The solution to the system of equations, is: (-2, 3).

Solution to System of Equations

To find the solution, you can use the elimination method by first making both equations equivalent. Then add or subtract to eliminate a variable.

Given:

• 4x + 5y = 7 --> Eqn. 1
• 3x – 2y = –12 --> Eqn. 2

Multiply eqn. 1 by 3 and eqn. 2 by 4:

12x + 15y = 21 --> Eqn. 1

12x – 8y = –48 --> Eqn. 2

• Subtract:

23y = 69

• Divide both sides by 23

y = 3

Substitute y = 3 into eqn. 1.

4x + 5(3) = 7

4x + 15 = 7

4x = 7 - 15

4x = -8

x = -2

Therefore, the solution to the system of equations, is: (-2, 3).

Learn more about the system of equations on:

https://brainly.com/question/13729904