2. Solving Systems Using Substitution - 6. Systems of Equations and Inequalities

When solving a system of equations using substitution, there are three steps to follow.

Isolate a variable in one of the equations.
Substitute the expression for that variable into the other equation and solve.
Substitute this solution into one of the equations and solve for the value of the other variable.

For this exercise, x is already isolated in one equation, so we can skip straight to solving!

4y=x & (I) 3x-y=70 & (II)

Substitute

(II):x= 4y

4y=x 3( 4y)-y=70

Multiply

(II):Multiply

4y=x 12y-y=70

SubTerm

(II):Subtract term

4y=x 11y=70

DivEqn

(II): .LHS /11.=.RHS /11.

4y=x y= 7011

Now, to find the value of x, we need to substitute y= 7011 into either one of the equations in the given system. Let's use the first equation.

4y=x y= 7011

Substitute

(I):y= 70/11

4( 7011)=x y= 7011

Multiply

(I): Multiply

28011=x y= 7011

RearrangeEqn

(I): Rearrange equation

x= 28011 y= 7011

The solution to this system of equations is the point ( 28011, 7011). We can also rewrite these solutions as mixed numbers.

x= 28011 y= 7011

▼

(I): Write fraction as a mixed number

WriteSum

(I): Write as a sum

x= 275+511 y= 7011

SplitIntoFactors

(I): Split into factors

x= 25(11)+511 y= 7011

FracToMixed

(I): Write fraction as a mixed number

x=25 511 y= 7011

▼

(II): Write fraction as a mixed number

WriteSum

(II): Write as a sum

x=25 511 y= 66+411

SplitIntoFactors

(II): Split into factors

x=25 511 y= 6(11)+411

FracToMixed

(II): Write fraction as a mixed number

x=25 511 y=6 411

Checking Our Answer

To check our answer, we will substitute our solution into both equations. If doing so results in true statements, then our solution is correct.

4y=x & (I) 3x-y=70 & (II)

(I), (II): x= 280/11, y= 70/11

4( 7011)? = 28011 3( 28011)- 7011? =70

(I), (II): Multiply

28011= 28011 84011- 7011? =70

SubFrac

(II): Subtract fractions

28011= 28011 77011? =70

CalcQuot

(II): Calculate quotient

28011= 28011 70=70

Because both equations are true statements, we know that our solution is correct.

Exercise 1 Page 375

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