The answer has one solution:
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→ x = 6 ; y = 7 ; or, write as: [6, 7].
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Step-by-step 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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