# How do you write the the ordered pair that is the solution to the following system of equations: -3x + y = 4 and -7x + y = 12?

Jan 5, 2018

Solve for one variable and substitute

#### Explanation:

Subtract the two equations from each other to eliminate the 'y' variable.
$\left(- 3 x + y = 4\right)$ $-$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .}$ $\leftarrow$ Subtracting a (-) by a (-) gives a (+).
$\left(- 7 x + y = 12\right)$

$4 x = - 8$

$x = - 2$

Plug in $- 2$ into one of the two equations to solve for $y$.

$- 3 \left(- 2\right) + y = 4$

$y = - 2$

The solution is $\left(- 2 , - 2\right)$

Jan 5, 2018

The point of intersection is $\left(- 2 , - 2\right)$.

#### Explanation:

Given:

Equation 1: $- 3 x + y = 4$

Equation 1: $- 7 x + y = 12$

I will use substitution to solve this system of equations. The ordered pair that is the solution is the point at which the two lines intersect.

Solve Equation 1 for $y$.

$- 3 x + y = 4$

Add $3 x$ to both sides and simplify.

$y = 3 x + 4$

Substitute $3 x + 4$ for $y$ in Equation 2 an d solve for $x$.

$- 7 x + y = 12$

$- 7 x + 3 x + 4 = 12$

Simplify.

$- 4 x + 4 = 12$

Subtract $4$ from both sides.

$- 4 x = 12 - 4$

Simplify.

$- 4 x = 8$

Divide both sides by $- 4$.

$x = \frac{8}{- 4}$

Simplify.

$x = - 2$

Substitute $- 2$ for $x$ in Equation 1 and solve for $y$.

$- 3 x + y = 4$

$- 3 \left(- 2\right) + y = 4$ $\leftarrow$ Two negatives make a positive.

Simplify.

$6 + y = 4$

Subtract $6$ from both sides.

$y = 4 - 6$

$y = - 2$

Point of Intersection: $\left(- 2 , - 2\right)$

graph{(y-3x-4)(y-7x-12)=0 [-11.25, 11.25, -5.625, 5.625]}