Question

Solve the system of equations by using the substitution method. List the solution as an ordered pair.

9x+4y=13

6x+5y=32

Answer 1

We have 9x+4y=13…(1) and 6x+5y=32…(2). From the 1^st equation, we have 4y = 13-9x so that y = 13/4 – 9x/4.

On substituting this value of y in the 2^nd equation, we get 6x +5(13/4–9x/4)=32 or, 6x+65/4-45x/4=32 or, 6x-45x/4 =32 -65/4 or, -21x/4= 63/4 so that x = (63/4)*(-4/21) =              -3. Then y =13/4 – 9x/4 = 13/4 -9*(-3)/4 = 13/4+27/4 = 10.

Thus x = -3 and y = 10. We can substitute these values of x and y in either of the equations to verify the result.