Solve each system of equations using any of the following methods: substitution,

Question

elimination, echelon, or Gauss-Jordan. If there are no solutions, say so. If there are an
infinite number of solutions, parametrize the answer using y as the parameter.
(a) x − 4y = −15
−2x + y = −19

Answer 1

First, solve the second equation for y:

-2x + y = -19

y = 2x - 19

Then substitute this expression for y into the first equation:

x - 4(2x-19) = -15

Simplify and solve for x:

x - 8x + 76 = -15

-7x = -91

x = 13

Now use this value of x to find y:

y = 2x - 19 = 2(13) - 19 = 7

Therefore, the solution to the system is (x,y) = (13,7).