+37157 x-6y=10 and 2x-2y=10 Multiply BOTH sides of the first eq by -2 to get
12y-2x=-20 then add to the second equation to get
10y = -10
y=-1
Sustitute y=-1 into one of the equations
x- 6(-1) = 10
x+6 =10
x=4
+1904 \(x-6y=10\) \(2x-2y=10\)
There are two ways to do it: by substitution and by subtraction
By substitution using the first equation first:
\(x-6y=10\)
\(x=10+6y\)
Substitute the \(x\) in the second equation with \(10+6y\)
\(2(10+6y)-2y=10\)
\(20+12y-2y=10\)
\(20+10y=10\)
\(10y=-10\)
\(y=-1\)
Substitute the \(y\) in the first equation with \(-1\)
\(x-6(-1)=10\)
\(x+6=10\)
\(x=4\)
\((-1,4)\)
OR
Substitute the \(y\) in the second equation with \(-1\)
\(2x-2(-1)=10\)
\(2x+2=10\)
\(2x=8\)
\(x=4\)
\((-1,4)\)
By substitution using the first equation second:
\(x-6y=10\)
\(-6y=10-x\)
\(y=\frac{10-x}{-6}\)
Substitute the \(y\) in the second equation with \(\frac{10-x}{-6}\)
\(2x-2(\frac{10-x}{-6})=10\)
\(2x+\frac{10-x}{3}=10\)
\(\frac{10-x}{3}=10-2x\)
\(10-x=30-6x\)
\(-x=20-6x\)
\(-x+6x=20\)
\(5x=20\)
\(x=4\)
Substitute the \(x\) in the first equation with \(4\)
\(4-6y=10\)
\(-6y=6\)
\(y=-1\)
\((4,-1)\)
OR
Substitute the \(x\) in the second equation with \(4\)
\(2(4)-2y=10\)
\(8-2y=10\)
\(-2y=2\)
\(y=-1\)
\((4,-1)\)
By substitution using the second equation first:
\(2x-2y=10\)
\(2x=10+2y\)
\(x=\frac{10+2y}{2}\)
\(x=5+y\)
Substitute the \(x\) in the first equation with \(5+y\)
\(5+y-6y=10\)
\(5-5y=10\)
\(-5y=5\)
\(y=-1\)
Substitute the \(y\) in the second equation with \(-1\)
\(2x-2(-1)=10\)
\(2x+2=10\)
\(2x=8\)
\(x=4\)
\((4,-1)\)
OR
Substitute the \(y\) in the first equation with \(-1\)
\(x-6(-1)=10\)
\(x+6=10\)
\(x=4\)
\((4,-1)\)
By subtracton by subtracting the second equation from the first equation:
\(x-6y=10\)
- \(2x-2y=10\)
--------------------------
\(-x-4y=0\)
\(-x=0+4y\)
\(-x=4y\)
\(x=-4y\)
Substitute the \(x\) in the first equation with \(-4y\)
\(-4y-6y=10\)
\(-10y=10\)
\(y=-1\)
Substitute the \(y\) in the second equation with \(-1\)
\(2x-2(-1)=10\)
\(2x+2=10\)
\(2x=8\)
\(x=4\)
\((4,-1)\)
OR
Substitute the \(x\) in the second equation with \(-4y\)
\(2(-4y)-2y=10\)
\(-8y-2y=10\)
\(-10y=10\)
\(y=-1\)
Substitute the \(y\) in the first equation with \(-1\)
\(x-6(-1)=10\)
\(x+6=10\)
\(x=4\)
\((4,-1)\)
By subtracton by subtracting the first equation from the second equation:
\(2x-2y=10\)
- \(x-6y=10\)
--------------------------
\(x+4y=0\)
\(x=0-4y\)
\(x=-4y\)
Substitute the \(x\) in the first equation with \(-4y\)
\(-4y-6y=10\)
\(-10y=10\)
\(y=-1\)
Substitute the \(y\) in the second equation with \(-1\)
\(2x-2(-1)=10\)
\(2x+2=10\)
\(2x=8\)
\(x=4\)
\((4,-1)\)
OR
Substitute the \(x\) in the second equation with \(-4y\)
\(2(-4y)-2y=10\)
\(-8y-2y=10\)
\(-10y=10\)
\(y=-1\)
Substitute the \(y\) in the first equation with \(-1\)
\(x-6(-1)=10\)
\(x+6=10\)
\(x=4\)
\((4,-1)\)
