Step 1) Solve the first equation for xx:
4x + 3y = -44x+3y=−4
4x + 3y - color(red)(3y) = -4 - color(red)(3y)4x+3y−3y=−4−3y
4x + 0 = -4 - 3y4x+0=−4−3y
4x = -4 - 3y4x=−4−3y
(4x)/color(red)(4) = (-4 - 3y)/color(red)(4)4x4=−4−3y4
(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = -4/4 - (3y)/4
x = -1 - 3/4y
Step 2) Substitute -1 - 3/4y for x in the second equation and solve for y:
3(-1 - 3/4y) - 7y = 34
-3 - 9/4y - 7y = 34
color(red)(3) - 3 - 9/4y - 7y = color(red)(3) + 34
-9/4y - 7y = 37
-9/4y - (4/4 xx 7)y = 37
-9/4y - 28/4y = 37
-37/4y = 37
-color(blue)(4)/color(red)(37) xx -37/4y = -color(blue)(4)/color(red)(37) xx 37
cancel(-color(blue)(4))/cancel(color(red)(37)) xx color(red)(cancel(color(black)(-37)))/color(blue)(cancel(color(black)(4)))y = -color(blue)(4)/cancel(color(red)(37)) xx color(red)(cancel(color(black)(37)))
y = -4
Step 3) Substitute -4 for y in the solution to the first equation at the end of Step 1 and calculate x:
x = -1 - (3/4 xx -4)
x = -1 - (3/color(red)(cancel(color(black)(4))) xx -color(red)(cancel(color(black)(4))))
x = -1 - (-3)
x = -1 + 3
x = 2
The solution to this problem is:
x = 2 and y = -4
