Question

SAT practice: Find the solution (x,y) to the system of equations below, what is the value of x-y (show work)

Answer 1

$7x + 3y = 8 \\ y = 2x - \frac{5}{3}$

Substitute the given value of x into the first equation

$7x + 3( 2x- \frac{5}{3} ) = 8$

To solve for x distribute 3 though the parentheses

$7x + 6x - 5 = 8$

Collect like terms

$13x - 5 = 8$

Move the constant to the right-hand side and change its sign

$13x = 8 + 5$

Add the numbers

$13x = 13$

Divide both sides of the equation by 13

$x = 1$

Now, Substitute the given value of x into the second equation

$y = 2x - \frac{5}{3}$

Plug in the value of x in the equation i.e. 1

$y = 2 \times 1 - \frac{5}{3}$

Any number multiplied by 1 results in number itself

$y = 2 - \frac{5}{3}$

Calculate the difference

$y = \frac{1}{3}$

The possible solution of the system is the ordered pair (x,y)

$(x,y)=(1, \frac{1}{3} )$