Question

What is the solution of the system of equations? Enter the solution as an ordered pair (use decimal rounded to the nearest hundredth if necessary) LaTeX: \begin{matrix}y=\frac{3}{2}x+\frac{5}{4}\\-2x+8y=-25\end{matrix}

Answer 1

(3/2, 7/2)

Explanation:

Given the system of equations;

y = 3x/2 + 5/4..... 1

-2x + 8y = 25 .... 2

Substitute equation 1 into 2;

From 2;

-2x + 8y = 25

-2x + 8(3x/2 + 5/4) = 25

-2x + 12x + 10 = 25

10x = 25 - 10

10x = 15

x = 15/10

x = 3/2

Substitute x = 3/2 into equation 1

From 1;

y = 3x/2 + 5/4

y = 3/2(3/2) + 5/4

y = 9/4 + 5/4

y = 14/4

y = 7/2

Hence the solution to the equation is (x, y) = (3/2, 7/2)