Question

The x coordinate of the solution to the system of equations y=x+4 and 3y=-2x+2

Answer 1

The x coordinate of the solution is -2

Explanation:

* To find the x-coordinate of the solution to the system of the

equations y = x + 4 and 3y = -2x + 2 solve the equations by the

substitution method

- In the substitution method we substitute one of the two variables

by the other to make an equation of one variable

∵ y = x + 4 ⇒ (1)

∵ 3y = -2x + 2 ⇒ (2)

- Substitute the value of y in equation (2) by the value of y in equation (1)

∵ The value y = 4 + x in the equation (1)

- Put this value of y in the equation (2)

∴ 3(x + 4) = -2x + 2 ⇒ open the bracket

∴ 3x + 12 = -2x + 2 ⇒ subtract 12 from both sides

∴ 3x = -2x - 10 ⇒ add 2x to both sides

∴ 5x = -10 ⇒ divide both sides by 5

∴ x = -2

* The x coordinate of the solution is -2

Answer 2

Hello!

The answer is:

The x-coordinate of the solution to the system of equations is:

`x=-2`

Why?

We can solve the problem writing both equations as a system of equations.

So, we are given the equations:

`\left \{ {{y=x+4} \atop {3y=-2x+2}} \right.`

Then, solving by reduction we have:

Multiplying the first equation by 2 in order to reduce the variable "x", we have:

`\left \{ {{2y=2x+2*4} \atop {3y=-2x+2}} \right.`

`5y=2x-2x+8+2\\\\5y=8+2\\\\y=(10)/(5)=2`

Now, substituting "y" into the first equation, to isolate "x" we have:

`y=x+4\\\\2=x+4\\\\x=2-4=-2`

Hence we have that the x-coordinate of the solution to the system of equations is

`x=-2`

Have a nice day!