Answer: x= - 3; y = -4
Step-by-step explanation:
-x + y = -7
-3x - y = -5
-4x = -12
x= -12 /- 4
x= - 3
-x + y = -7
-(-3) + y = - 7
3 + y = - 7
y = - 7 + 3
y = -4
-x + y = -7
-3 - 4 = - 7
- 7 = - 7
Answer:
y = -4, x = 3
Step-by-step explanation:
-x + y = -7
-3x - y = -5
Isolate x for -x + y = -7.
-x + y = -7
Subtract y from both sides.
-x + y - y = -7 - y
Simplify.
-x = -7 - y
Divide both sides by -1
[tex]\frac{-x}{-1} =-\frac{7}{-1} -\frac{y}{-1}[/tex]
[tex]\frac{-x}{-1}[/tex]
Apply the fraction rule: [tex]\frac{-a}{-b} =\frac{a}{b}[/tex]
[tex]=\frac{x}{1}[/tex]
Apply rule: [tex]\frac{a}{1} =a[/tex]
[tex]=x[/tex]
Simplify [tex]-\frac{7}{-1} -\frac{y}{-1}[/tex]
[tex]-\frac{7}{-1} -\frac{y}{-1}[/tex]
Apply rule: [tex]\frac{a}{c} ±\frac{b}{c} =\frac{a±b}{c}[/tex]
[tex]=-\frac{7}{-1} -\frac{y}{-1}[/tex]
Apply the fraction rule: [tex]\frac{a}{-b} =-\frac{a}{b}[/tex]
[tex]=\frac{-7-y}{1}[/tex]
Apply rule: [tex]\frac{a}{1} =a[/tex]
[tex]=-(-y-7)[/tex]
Distribute parentheses.
[tex]=-(-7)-(-y)[/tex]
Apply minus - plus rule.
[tex]-(-a)=a[/tex]
[tex]=7+y[/tex]
[tex]x=7+y[/tex]
Substitute [tex]x=7+y[/tex]
[tex][-3(7+y)-y=-5][/tex]
Isolate y for [tex]-3(7+y)-y=-5[/tex]
[tex]-3(7+y)-y=-5[/tex]
Expand -3 (7 + y )
-3 (7 + y )
Apply the distributive law: [tex]a(b+c)= ab+ac[/tex]
[tex]a=-3,b=7, c=y[/tex]
[tex]=-3*7+(-3)y[/tex]
Apply minus - plus rule
[tex]+(-a)=-a[/tex]
[tex]=-3*7-3y[/tex]
Multiply the numbers: 3 * 7 = 21
[tex]=-21-3y[/tex]
[tex]-21-3y-y=-5[/tex]
Add similar elements: [tex]-3-y=-4y[/tex]
[tex]-21-4y=-5[/tex]
Add 21 to both sides.
[tex]-21-4y+21=-5+21[/tex]
Simplify.
[tex]-4y=16[/tex]\
Divide both sides by -4
[tex]\frac{-4y}{-4} =\frac{16}{-4}[/tex]
Simplify [tex]\frac{-4y}{-4} =\frac{16}{-4}[/tex]
Simplify [tex]\frac{-4y}{-4}[/tex]
Apply the fraction rule: [tex]\frac{-a}{-b}=-\frac{a}{b}[/tex]
[tex]=-\frac{16}{4}[/tex]
Divide the numbers: [tex]\frac{16}{4} =4[/tex]
= - 4
y = -4
For x = 7 + y, substitute y = -4
x = 7 - 4
Subtract the numbers: 7 - 4 = 3
= 3
x = 3
y = -4, x = 3
[tex](3,-4)[/tex]
