Question

How many solutions does the system have?

You can use the interactive graph below to find the answer.
y=x+1
y = 2x – 5
Choose 1 answer:

Answer 1

The answer has one solution:

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→ x = 6 ; y = 7 ; or, write as: [6, 7].

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Explanation:

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Given:

y = x + 1;

y = 2x – 5 ;

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2x – 5 = x + 1 ; Solve for "x" ;

Subtract "x" ; and Subtract "1" ; from Each Side of the equation:

2x – x – 5 – 1 = x – x + 1 – 1 ;

to get:

x – 6 = 0 ;

Now, add "6" to Each Side of the equation;

to isolate "x" on one side of the equation;

and to solve for "x" :

x – 6 + 6 = 0 + 6 ;

to get:

x = 6 .

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Now, let us solve for "y" ;

We are given:

y = x + 1 ;

Substitute our solved value for "x" ; which is: "6" ; for "x" ; into this given equation; to obtain the value for "y" :

y = x + 1 ;

= 6 + 1 ;

y = 7 .

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Let us check our answers by plugging the values for "x" and "y" ;

("6" ; and "7"; respectively); into the second given equation; to see if these values for "x" and "y" ; hold true:

Given: y = 2x – 5 ;

→ 7 =? 2(6) – 5 ?? ;

→ 7 =? 2(6) – 5 ?? ;

→ 7 =? 12 – 5 ?? ;

→ 7 =? 7 ?? ;

→ Yes!

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The answer has one solution:

→ x = 6 ; y = 7 ; or, write as: [6, 7].

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Hope this is helpful! Best wishes!

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