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# 5x - 4y = 14, x - 2y = -2

5x - 4y = 14, x - 2y = -2

SUBSTITUTION:

Solve the first for x and plug it into the second

x=-2+2y

5(-2+2y) -4y=14

-10+10y-4y=14

6y=14+10

6y=24

or,y=24/6

y=4

Putting the value of Y in first equation:

x-2(4)=-2

x-8=-2

x=-2+8

x=6

Remember that substitution involves getting one equation to express one of the variables in terms of the other and then plugging that expression in to your remaining equation.

Out of the two equations you listed, you can make it easier on yourself by choosing to use the one that already has one of the variables multiplied by one.

In this case:

x -2y = -2 can be rearranged by adding 2y to each side to yield:

x = 2y-2

Now substitute that expression into the other equation in place of x to get:

5x - 4y = 14 where x = 2y -2 becomes

5(2y-2) - 4y = 14

Multiply through your parentheses to then get:

10y - 10 - 4y = 14

now add 10 to both sides and subtract 4y from 10y

6y = 24 and then y = 4

Now you know from the previous equation you used that

x = 2y - 2 so that x = 2(4) - 2 = 6

5(6) - 4(4) = 14

30 - 16 = 14

14 = 14

and

6 - 2(4) = -2

6 - 8 = -2

-2 = -2