How do you solve y-6x=22y6x=22 and 4y+17=-11x4y+17=11x using substitution?

2 Answers
May 17, 2018

x = -3x=3
y = 4y=4

Explanation:

Solving through Substitution

y - 6x = 22y6x=22
4y + 17 = -11x4y+17=11x

First, we want to solve for a variable that can be easily found. Then, we'll plug the variable in to solve for the variables. Let's start with finding what y is since it looks easy to solve for.

y - 6x = 22y6x=22

Add 6x to both sides to negate -6x6x. This'll give us yy's value. You should now have:

y = 6x + 22y=6x+22

Substitute in this value for y in the second equation to solve for the variables:

4y + 17 = -11x4y+17=11x
4(6x + 22) + 17 = -11x4(6x+22)+17=11x

Distribute.

24x + 88 + 17 = -11x24x+88+17=11x

Combine like terms. 88 + 1788+17 is 105105, so:

24x + 105 = -11x24x+105=11x

Subtract 24x24x from both sides to negate 24x24x in order to solve for x. The reason why we aren't adding 11x11x to both sides is because it'll make the equation unbalanced. -11x - 24x11x24x is basically the same as 11 + 24 11+24because they're the same sign, so they combine to become -35x35x. So:

105 = -35x105=35x

Divide by -35 to solve for x.

105/-3510535 = xx

x = -3x=3

Now, plug this variable back into this equation to solve for y:

y = 6x + 22y=6x+22
y = 6(-3) + 22y=6(3)+22

Distribute.

y = -18 + 22y=18+22

Add.
y = 4y=4

Confirm this by plugging it back into the two equations:

y - 6x = 22y6x=22
4 - 6(-3) = 2246(3)=22

Distribute.

4 + 18 = 224+18=22
22 = 2222=22

4y + 17 = -11x4y+17=11x
4(4) + 17 = -11(-3) 4(4)+17=11(3)16 + 17 = 33 33 = 33#

Confirmed: these are the correct variables.

May 17, 2018

See a solution process below:

Explanation:

Step 1) Solve the first equation for yy:

y - 6x + color(red)(6x) = 22 + color(red)(6x)y6x+6x=22+6x

y - 0 = 22 + 6xy0=22+6x

y = 22 + 6xy=22+6x

Step 2) Substitute (22 + 6x)(22+6x) for yy in the second equation and solve for xx:

4y + 17 = -11x4y+17=11x becomes:

4(22 + 6x) + 17 = -11x4(22+6x)+17=11x

(4 * 22) + (4 * 6x) + 17 = -11x(422)+(46x)+17=11x

88 + 24x + 17 = -11x88+24x+17=11x

88 + 17 + 24x = -11x88+17+24x=11x

105 + 24x = -11x105+24x=11x

105 - color(red)(105) + 24x + color(blue)(11x) = -11x + color(blue)(11x) - color(red)(105)105105+24x+11x=11x+11x105

0 + (24 + color(blue)(11))x = 0 - 1050+(24+11)x=0105

35x = -10535x=105

(35x)/color(red)(35) = -105/color(red)(35)35x35=10535

(color(red)(cancel(color(black)(35)))x)/cancel(color(red)(35)) = -3

x = -3

Step 3) Substitute -3 for x in the solution to the first equation at the end of Step 1 and calculate y;

y = 22 + 6x becomes:

y = 22 + (6 xx -3)

y = 22 - 18

y = 4

The Solution Is:

x = -3 and y = 4

Or

(-3, 4)