Solved on Feb 18, 2024

Find the missing value in the solution to the linear equation $4x + y = 10$ , given the point $(\quad, -6)$ .

STEP 1

Assumptions
1. We are given a linear equation in two variables: $4x + y = 10$ .
2. We are given a partial solution to the equation in the form of a point with the y-coordinate of $-6$ and an unknown x-coordinate.
3. We need to find the x-coordinate that, along with the given y-coordinate, satisfies the equation.

STEP 2

We will substitute the given y-coordinate into the equation to find the corresponding x-coordinate.
$4x + y = 10$
$4x + (-6) = 10$

STEP 3

Now, we solve for $x$ by isolating it on one side of the equation.
$4x - 6 = 10$

STEP 4

Add $6$ to both sides of the equation to move the constant term to the right side.
$4x - 6 + 6 = 10 + 6$

STEP 5

Simplify both sides of the equation.
$4x = 16$

STEP 6

Divide both sides of the equation by $4$ to solve for $x$ .
$\frac{4x}{4} = \frac{16}{4}$

STEP 7

Calculate the value of $x$ .
$x = 4$
The complete solution to the equation with the given y-coordinate of $-6$ is $(4, -6)$ .

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Find the missing value in the solution to the linear equation $4x + y = 10$ , given the point $(\quad, -6)$ .

STEP 1

STEP 2

We will substitute the given y-coordinate into the equation to find the corresponding x-coordinate.
$4x + y = 10$
$4x + (-6) = 10$

STEP 3

Now, we solve for $x$ by isolating it on one side of the equation.
$4x - 6 = 10$

STEP 4

Add $6$ to both sides of the equation to move the constant term to the right side.
$4x - 6 + 6 = 10 + 6$

STEP 5

Simplify both sides of the equation.
$4x = 16$

STEP 6

Divide both sides of the equation by $4$ to solve for $x$ .
$\frac{4x}{4} = \frac{16}{4}$

STEP 7

Calculate the value of $x$ .
$x = 4$
The complete solution to the equation with the given y-coordinate of $-6$ is $(4, -6)$ .

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Find the missing value in the solution to the linear equation 4x+y=104x + y = 104x+y=10, given the point (,−6)(\quad, -6)(,−6).

STEP 1

STEP 2

We will substitute the given y-coordinate into the equation to find the corresponding x-coordinate.4x+y=104x + y = 104x+y=104x+(−6)=104x + (-6) = 104x+(−6)=10

STEP 3

Now, we solve for xxx by isolating it on one side of the equation.4x−6=104x - 6 = 104x−6=10

STEP 4

Add 666 to both sides of the equation to move the constant term to the right side.4x−6+6=10+64x - 6 + 6 = 10 + 64x−6+6=10+6

STEP 5

Simplify both sides of the equation.4x=164x = 164x=16

STEP 6

Divide both sides of the equation by 444 to solve for xxx.4x4=164\frac{4x}{4} = \frac{16}{4}44x​=416​

STEP 7

Calculate the value of xxx.x=4x = 4x=4The complete solution to the equation with the given y-coordinate of −6-6−6 is (4,−6)(4, -6)(4,−6).

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Find the missing value in the solution to the linear equation $4x + y = 10$ , given the point $(\quad, -6)$ .

We will substitute the given y-coordinate into the equation to find the corresponding x-coordinate.
$4x + y = 10$
$4x + (-6) = 10$

Now, we solve for $x$ by isolating it on one side of the equation.
$4x - 6 = 10$

Add $6$ to both sides of the equation to move the constant term to the right side.
$4x - 6 + 6 = 10 + 6$

Simplify both sides of the equation.
$4x = 16$

Divide both sides of the equation by $4$ to solve for $x$ .
$\frac{4x}{4} = \frac{16}{4}$

Calculate the value of $x$ .
$x = 4$
The complete solution to the equation with the given y-coordinate of $-6$ is $(4, -6)$ .