Question

Solve the system of equations by the substitution method.



Choose one answer.
a. (1, 10)
b. (10, 1)
c. infinite number of solutions
d. no solution

Answer 1

First thing to do is to multiply out where required and combine terms.

The first equation written out is:

-6y + 7y = -4x + 4x + 8 + 4x -2

y = 4x + 6

4x -y = -6, label this equation one

4(x + y) - x + y = 53:

becomes 3x + 5y = 53, label equation 2


You have two unknowns and two equations. To find x, y must be eliminated and x must be eliminated to find y. Actually once you find x or y you can substitute that value in to find the other.

To eliminate x, equation 1 would have to be multiplied by 3 and equation 2 would have to be multiplied by -4 to have 12x in equation 1 and -12x in equation 2. That is a little more complicated.

It is easier to eliminate y.

All that needs to be done is to multiply equation 1 by 5 and add it to equation 2.

Multiply 1 by -5 and add to 2.

20x -5y = -30, equation one

3x + 5y = 53, equation two

Combined equation is:

23x = 23

Divide by 23:

x = 1

Substiturt x into either equation:

Pick equation one since the coefficients are lower values:

4 * (1) - y = -6

4 - y = -6

-y = -6 - 4

- y = -10

both sides are negative so the negative sign can be removed from both sides:

y = 10 and x = 1