Question

-5x + 4y = -22
-3x – 4y = -26

Answer 1

Answer:

x = 6

y = 2

Step-by-step explanation:

Solve for x in the first equation:

-5x + 4y = -22

Step 1 - Subtract 4y from both sides:

-5x + 4y - 4y = -22 - 4y

-5x = -22 - 4y

Step 2 - Change every operation to its opposite counterpart:

5x = 22 + 4y

Divide both sides by 5:

 $\frac{5x}{5} =\frac{ (22 + 4y) }{5}$

$x = \frac{ (22 + 4y) }{5}$

Step 3 - Now substitute this into the second equation:

-3x - 4y = -26

-3( $\frac{ (22 + 4y) }{5}$) - 4y = -26

-3($\frac{1}{5}(22+4y)$)

$\frac{-3}{1} * \frac{1}{5} = \frac{-3}{5}$

$\frac{-3}{5}(22 + 4y) - 4y = -26$

Step 4 - Multiply both sides by 5:

$-3(22 + 4y) - 5(4y) = -(5)26\\-3(22 + 4y) - 20y = -130$

Step 5 - Simplify the brackets

$-66 -12y - 20y = -130$

130 = 66 + 12y + 20y

130 = 66 + 32y

Step 6 - Subtract 66 from both sides of the equation;

130 - 66 = 66 + 32y - 66

64 = 32y

Step 7 - Divide both sides by 32:

$\frac{64}{32} = \frac{32y}{32}$

2 = y

Step 8 - So y  = 2, so now we can substitute this into one of the equations:

-5x + 4y = -22

-5x + 4(2) = -22

-5x + 8 = -22

Subtract 8 from both sides

-5x + 8 - 8 = -22 - 8

-5x = -30

5x = 30

Divide both sides by 5:

$\frac{5x}{5} = \frac{30}{5}$

x = 6

Hope this helps!