Question

What is the solution to the system of equations?

Answer 1

Answer:

(7, 13/3)

Step-by-step explanation:

$y=\frac{1}{3} x+2$   Line up the equations on top of each other

$y=\frac{4}{3} x-5$

$-4*[y=\frac{1}{3} x+2]$   Multiply the top equation by $-4$ in order to cancel out the $x$ variable

$-4y=-\frac{4}{3} x-8$   Switch out the first equation for this one

$-4y=-\frac{4}{3} x-8$   Line up the equations

    $y=\frac{4}{3} x-5$

$-3y=-13$   Add the two equations top to bottom, left to right

    $y=\frac{13}{3}$

Now that you've found $y$, you need to find $x$. Just plug in the y-value to either of the equations in Step 1:

The first equation has smaller numbers, so let's use that one.

$\frac{13}{3} =\frac{1}{3} x+2$

To make it easier you can multiply all the terms in the equation by 3:

$13=x+6$

 $7=x$

The $x$- and $y$- values together give a solution of ( $7$, $\frac{13}{3}$ )

Answer 2

Solve systems of equations by graphing. A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system.